Question 1: Palette 1/345

Allen 2000 MCQ

The maximum range of a projectile fired with some initial velocity is found to be 2000 m. The maximum height (H) reached by this projectile is:

A

250 metre

B

500 metre

C

1000 metre

D

2000 metre

Question 2: Palette 2/345

Allen 2000 MCQ

A bullet is fired from a gun at the speed of $280 \, ms^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is $(g = 9.8 \, \text{ms}^{-2}, \sin 30^{\circ} = 0.5)$ :-

A

2000 m

B

1000 m

C

3000 m

D

2800 m

Question 3: Palette 3/345

Allen MCQ

If displacement of a particle is zero, the distance covered:

A

must be zero

B

may or may not be zero

C

cannot be zero

D

depends upon the particle

Question 4: Palette 4/345

Allen MCQ

If the distance covered is zero, the displacement:

A

must be zero

B

may or may not be zero

C

cannot be zero

D

depends upon the particle

Question 5: Palette 5/345

Allen MCQ

The location of a particle is changed. What can we say about the displacement and distance covered by the particle:

A

Both cannot be zero

B

One of the two may be zero

C

Both must be zero

D

If one is positive, the other is negative and vice-versa

Question 6: Palette 6/345

Allen MCQ

The numerical ratio of distance to the displacement covered is always :-

A

less than one

B

equal to one

C

equal to or less than one

D

equal to or greater than one

Question 7: Palette 7/345

Allen MCQ

Milkha Singh can cover one round of a circular park in 40 second, After 1 minute and 40 second, he will cover a distance and displacement respectively (R = Radius of circle):-

A

Zero, Zero

B

$4\pi \mathrm{R}$ , R

C

$5\pi \mathrm{R}$ , 2R

D

$6\pi \mathrm{R}$ , 2R

Question 8: Palette 8/345

Allen MCQ

A hall has the dimensions $10 \, m \times 10 \, m \times 10 \, m$ . A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its displacement is nearly

A

$5\sqrt{3} \, m$

B

$10\sqrt{3} \, m$

C

$20\sqrt{3} \, m$

D

$30\sqrt{3} \, m$

Question 9: Palette 9/345

Allen MCQ

An ant is scramping on the stairs as shown in the figure. There are '4' stairs and each stair has width of 12 cm and height of 5 cm. The distance travelled by the ant to scramp the stairs is :-

A

$52\mathrm{cm}$

B

$68\mathrm{cm}$

C

$48\mathrm{cm}$

D

$20\mathrm{cm}$

Question 10: Palette 10/345

Allen MCQ

An insect starts climbing a conical birthday hat of radius 5 cm at base. It starts from point A and reaches point B, taking spiral path on the hat. Find out its displacement if height is 12 cm:-

A

$12\mathrm{cm}$

B

$8\mathrm{cm}$

C

$13\mathrm{cm}$

D

$25\mathrm{cm}$

Question 11: Palette 11/345

Allen MCQ

Three particles P, Q and R are situated at point A on the circular path of radius 10 m. All three particles move along different paths and reach point B as shown in figure. Then the ratio of distance traversed by particles P and R is :

A

$\frac{3}{4}$

B

$\frac{3}{1}$

C

$\frac{3\pi}{4}$

D

$\frac{\pi}{3}$

Question 12: Palette 12/345

Allen MCQ

A body moves along the curved path of a semi circle. Calculate the ratio of distance to displacement:

A

11:7

B

7:11

C

$11:\sqrt{2} \times 7$

D

$7:11\sqrt{2}$

Question 13: Palette 13/345

Allen MCQ

Distance travelled by the tip of minute hand of length 10 cm in 100 sec is

A

$\frac{\pi}{180}$ m

B

$\frac{\pi}{360}$ m

C

$\frac{\pi}{1200}$ m

D

$\frac{3\pi}{2160}$ m

Question 14: Palette 14/345

Allen MCQ

If a particle moves from point P(2, 3, 5) to point Q(3, 4, 5). Its displacement vector be :-

A

$\hat{\mathbf{i}} + \hat{\mathbf{j}} + 10\hat{\mathbf{k}}$

B

$\hat{\mathbf{i}} + \hat{\mathbf{j}} + 5\hat{\mathbf{k}}$

C

$\hat{\mathbf{i}} + \hat{\mathbf{j}}$

D

$2\hat{\mathbf{i}} + 4\hat{\mathbf{j}} + 6\hat{\mathbf{k}}$

Question 15: Palette 15/345

Allen MCQ

A man walks 30 m towards north, then 20 m towards east and the last $30\sqrt{2}$ m towards south-east. The displacement from origin is:

A

10 m towards west

B

50 m towards east

C

$60\sqrt{2}$ m towards north west

D

$60\sqrt{2}$ m towards east north

Question 16: Palette 16/345

Allen MCQ

A person walks 80 m east, then turns right through angle $143^{\circ}$ walks further 50 m and stops. His position relative to the starting point is

A

50 m, $53^{\circ}$ east of south

B

50 m, $53^{\circ}$ south of east

C

30 m, $37^{\circ}$ south of east

D

30 m, $53^{\circ}$ south of east

Question 17: Palette 17/345

Allen MCQ

A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward, followed by 5 steps forward and 3 steps backward and so on. Each step is one meter long and takes one second. There is a pit on the road 13 meters away from the starting point. The drunkard will fall into the pit after:

A

29 s

B

21 s

C

37s

D

31 s

Question 18: Palette 18/345

Allen MCQ

A train covers the first half of the distance between two stations with a speed of 30 km/h and the other half with 70 km/h. Then its average speed is:

A

50 km/h

B

48 km/h

C

42 km/h

D

100 km/h

Question 19: Palette 19/345

Allen MCQ

Select the correct statements from the following. S1. Average velocity is path length divided by time interval. S2. In general, average speed ≥ |average velocity| S3. A particle moving in a given direction with a non-zero velocity can have zero speed. S4. The magnitude of average velocity is the average speed.

A

S₁

B

S₂

C

S₃

D

S₄

Question 20: Palette 20/345

Allen MCQ

The magnitude of average velocity is equal to the average speed when a particle moves :

A

on a curved path

B

in the same direction

C

with constant acceleration

D

with constant retardation

Question 21: Palette 21/345

Allen MCQ

A man walks for some time 't' with velocity (v) due east. Then he walks for same time 't' with velocity (v) due north. The average speed of the man is:

A

2v

B

$\sqrt{2}$ v

C

v

D

$\frac{v}{\sqrt{2}}$

Question 22: Palette 22/345

Allen MCQ

A car travels a distance $d$ on a straight road in two hours and then returns to the starting point in next three hours. Its average speed and average velocity is:

A

$\frac{d}{5}, 0$

B

$\frac{2d}{5}, 0$

C

$\frac{5d}{6}, \frac{d}{5}$

D

none of these

Question 23: Palette 23/345

Allen MCQ

A particle moves in the east direction with 15 m/sec for 2 sec then northwards with 5 m/s for 8 sec. Average velocity of the particle is:-

A

1 m/s

B

5 m/s

C

7 m/s

D

10 m/s

Question 24: Palette 24/345

Allen MCQ

A man walks on an equilateral triangle along path ABC with constant speed then the ratio of average speed and magnitude of average velocity for A to C :-

A

1

B

2

C

$\frac{1}{2}$

D

None

Question 25: Palette 25/345

Allen MCQ

A car runs at constant speed on a circular track of radius 10 m taking 6.28s on each lap (i.e. round). The average speed and average velocity for half lap is :

A

Velocity $20/\pi$ m/s, speed 10 m/s

B

Velocity zero, speed 10 m/s

C

Velocity zero, speed zero

D

Velocity 10 m/s, speed zero

Question 26: Palette 26/345

Allen MCQ

A particle moves in straight line in same direction for 20 sec. with velocity $3\mathrm{m / s}$ and then moves with velocity $4\mathrm{m / s}$ for another 20 sec. and finally moves with velocity $5\mathrm{m / s}$ for next 20 sec. What is the average velocity of the particle?

A

$3\mathrm{m / s}$

B

$4\mathrm{m / s}$

C

$5\mathrm{m / s}$

D

Zero

Question 27: Palette 27/345

Allen MCQ

An object travels 10 km at a speed of 100 m/s and another 10 km at 50 m/s. The average speed over the whole distance is :-

A

75 m/s

B

55 m/s

C

66.7 m/s

D

33.3 m/s

Question 28: Palette 28/345

Allen MCQ

A body has speed V, 2V and 3V in first 1/3 part of total travelled distance S, second 1/3 part of S and third 1/3 part of S respectively. Its average speed will be :-

A

V

B

2V

C

$\frac{18}{11}\mathrm{V}$

D

$\frac{11}{18}\mathrm{V}$

Question 29: Palette 29/345

Allen MCQ

A body covers one-third of the time with a velocity $v_{1}$ the second one-third of the time with a velocity $v_{2}$ , and the last one-third of the time with a velocity $v_{3}$ . The average velocity is:

A

$\frac{v_{1} + v_{2} + v_{3}}{3}$

B

$\frac{3v_{1}v_{2}v_{3}}{v_{1}v_{2} + v_{2}v_{3} + v_{3}v_{1}}$

C

$\frac{v_{1}v_{2}+v_{2}v_{3}+v_{3}v_{1}}{3}$

D

$\frac{v_{1}v_{2}v_{3}}{3}$

Question 30: Palette 30/345

Allen MCQ

If a car cover $2/5^{th}$ of total distance with $v_{1}$ speed and $3/5^{th}$ distance with $v_{2}$ speed then the average speed is:

A

$\frac{1}{2}\sqrt{v_{1}v_{2}}$

B

$\frac{v_{1}+v_{2}}{2}$

C

$\frac{2v_{1}+v_{2}}{v_{1}+v_{2}}$

D

$\frac{5v_{1}v_{2}}{3v_{1}+2v_{2}}$

Question 31: Palette 31/345

Allen MCQ

A particle moving in a straight line covers half the distance with speed of 10 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is:

A

8.0 m/s

B

12.0 m/s

C

10.0 m/s

D

7.5 m/s

Question 32: Palette 32/345

Allen MCQ

A point object traverses half the distance with velocity $v_{0}$ . The remaining part of the distance is covered with velocity $v_{1}$ for the half time and with velocity $v_{2}$ for the rest half. The average velocity of the object for the whole journey is

A

$2\mathrm{v}_1(\mathrm{v}_0 + \mathrm{v}_2) / (\mathrm{v}_0 + 2\mathrm{v}_1 + 2\mathrm{v}_2)$

B

$2\mathrm{v}(\mathrm{v}_0 + \mathrm{v}_1) / (\mathrm{v}_0 + \mathrm{v}_1 + \mathrm{v}_2)$

C

$2\mathrm{v}_0(\mathrm{v}_1 + \mathrm{v}_2) / (\mathrm{v}_1 + \mathrm{v}_2 + 2\mathrm{v}_0)$

D

$2\mathrm{v}_2(\mathrm{v}_0 + \mathrm{v}_1) / (\mathrm{v}_1 + 2\mathrm{v}_2 + \mathrm{v}_0)$

Question 33: Palette 33/345

Allen MCQ

A scooter going due east at $10 \, ms^{-1}$ turns in right side through an angle of $90^{\circ}$ . If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is :-

A

$20.0 \, ms^{-1}$ in south-west direction

B

Zero

C

$10.0 \, ms^{-1}$ in south-east direction

D

$14.14 \, ms^{-1}$ in south-west direction

Question 34: Palette 34/345

Allen MCQ

A person is moving in a circle of radius r with constant speed V. The change in velocity in moving from A to B is

A

$2\mathrm{V}\cos 40^{\circ}$

B

$2\mathrm{V}\sin 40^{\circ}$

C

$2\mathrm{V}\cos 20^{\circ}$

D

$2\mathrm{V}\sin 20^{\circ}$

Question 35: Palette 35/345

Allen MCQ

An insect crawls a distance of 4m along north in 10 s and then a distance of 3m along east in 5 s. The average velocity of the insect is:

A

$\frac{7}{15}$ m/s

B

$\frac{1}{5}$ m/s

C

$\frac{1}{3}$ m/s

D

$\frac{4}{5}$ m/s

Question 36: Palette 36/345

Allen MCQ

The position x of a particle varies with time (t) as $x = at^{2} - bt^{3}$ . The velocity at time t of the particle will be equal to zero, where t is equal to:

A

$\frac{2a}{3b}$

B

$\frac{a}{b}$

C

$\frac{a}{3b}$

D

$\frac{a}{2b}$

Question 37: Palette 37/345

Allen MCQ

If x denotes displacement in time t and x = a sint, then acceleration is:

A

a cos t

B

- a cos t

C

a sin t

D

- a sin t

Question 38: Palette 38/345

Allen MCQ

The motion of a particle is described by the equation $x = a + bt^{2}$ where a = 15 cm and $b = 3 \, cm/sec^{2}$ . Its acceleration at time 3 sec will be :-

A

$36 \, cm/sec^{2}$

B

$18 \, cm/sec^{2}$

C

$6 \, cm/sec^{2}$

D

$32 \, cm/sec^{2}$

Question 39: Palette 39/345

Allen MCQ

Equation of displacement for a particle is $s = 3t^{3} + 7t^{2} + 14t + 8 \, m$ . Its acceleration at time t = 2 sec is :-

A

$10 \, m/s^{2}$

B

$16 \, m/s^{2}$

C

$25 \, m/s^{2}$

D

$50 \, m/s^{2}$

Question 40: Palette 40/345

Allen MCQ

A body is moving according to the equation $x = at^{2} + bt - c$ . Then its instantaneous speed is given by :-

A

$a + 2b + 3ct$

B

$a + 2bt - 3ct^{2}$

C

2b - 6ct

D

2at + b

Question 41: Palette 41/345

Allen MCQ

The relation $t = \sqrt{x} + 3$ describes the position of a particle where x is in meters and t is in seconds. The acceleration of particle is:

A

$2 \, m/s^{2}$

B

$4 \, m/s^{2}$

C

$5 \, m/s^{2}$

D

zero

Question 42: Palette 42/345

Allen MCQ

The displacement of a particle is given by $y = a + bt + ct^{3}$ . The initial velocity and acceleration are respectively:

A

b, 0

B

-b, 2c

C

b, 2c

D

2c, -4d

Question 43: Palette 43/345

Allen MCQ

Equation of a particle moving along the x axis is $x = u(t - 2) + a(t - 2)^{2}$

A

the initial velocity of the particle is u

B

the acceleration of the particle is a

C

the acceleration of the particle is 2a

D

at t = 2 particle is not at origin

Question 44: Palette 44/345

Allen MCQ

If for a particle position $x \propto t$ then:

A

velocity is constant

B

acceleration is non zero

C

acceleration is variable

D

None of these

Question 45: Palette 45/345

Allen MCQ

The velocity of a body depends on time according to the equation $= 20 + 0.1t$ . The body has:

A

uniform acceleration

B

uniform retardation

C

non-uniform acceleration

D

zero acceleration

Question 46: Palette 46/345

Allen MCQ

Which of the following relations representing velocity of a particle describes motion with constant acceleration?

A

v = 6 - 7 t

B

$v = 3t^{2} + 5t^{3} + 7$

C

$v = 9t^{2} + 8$

D

$v = 4t^{-2} + 3t^{-1}$

Question 47: Palette 47/345

Allen MCQ

Which of the following equations represents the motion of a body moving with constant finite velocity? in these equations, y denotes the displacement in time t and p, q and r are arbitrary constants:

A

$y = (p + qt)^{2} (r + pt)$

B

$y = p + tqr$

C

$y = (p + t)(q + t)(r + 1)$

D

$y = (p + qt)rt$

Question 48: Palette 48/345

Allen MCQ

The displacement of a particle starting from rest (at t=0) is given by $s = 6t^{2} - t^{3}$ The time when the particle will attain zero acceleration is :

A

2s

B

8s

C

12s

D

16s

Question 49: Palette 49/345

Allen MCQ

The displacement of a particle varies with time according to the relation $x = \frac{k}{b}[1 - e^{-bt}]$ . Then the velocity of the particle is:

A

$k(e^{-bt})$

B

$\frac{k}{b^{2}e^{-bt}}$

C

$kbe^{-bt}$

D

None of these

Question 50: Palette 50/345

Allen MCQ

A particle moves along a straight line such that its displacement at any time t is given by $s = t^{3} - 6t^{2} + 3t + 4$ metres. The displacement when the acceleration is zero is:

A

3 m

B

-12

C

42 m

D

-6 m

Question 51: Palette 51/345

Allen MCQ

Displacement x of a particle is related to time t as $x = at + bt^{2} - ct^{3}$ where a, b and c are constants. The velocity of the particle when its acceleration is zero is given by:

A

$a + \frac{b^{2}}{c}$

B

$a + \frac{b^{2}}{2c}$

C

$a + \frac{b^{2}}{3c}$

D

$a + \frac{b^{2}}{4c}$

Question 52: Palette 52/345

Allen MCQ

A particle moves along the curve $y = \frac{x^{2}}{2}$ . Here x varies with time as $x = \frac{t^{2}}{2}$ . Where x and y are measured in metre and t in second. At t = 2s, the velocity of the particle (in ms $^{-1}$ ) is:

A

$2\hat{i}-4\hat{j}$

B

$2\hat{i}+4\hat{j}$

C

$4\hat{i}+2\hat{j}$

D

$4\hat{i}-2\hat{j}$

Question 53: Palette 53/345

Allen MCQ

The velocity-time relation of an electron starting from rest is given by u = kt, where $k = 2 \, m/s^{2}$ . The distance traversed in 4 sec is:

A

9m

B

16 m

C

27 m

D

36 m

Question 54: Palette 54/345

Allen MCQ

The initial velocity of a particle is u (at t = 0) and the acceleration is given by f = at². Which of the following relations is valid?

A

$v = u + at^{2}$

B

$v = u + \frac{at^{2}}{2}$

C

$v = u + \frac{at^{3}}{3}$

D

$v = u + at$

Question 55: Palette 55/345

Allen MCQ

A particle is moving with a velocity of 10m/s towards east. After 20 s its velocity changes to 10m/s towards north. Its average acceleration is:-

A

zero

B

$\sqrt{2}$ m/s $^{2}$ towards N-W

C

$\frac{1}{\sqrt{2}}$ m/s $^{2}$ towards N-E

D

$\frac{1}{\sqrt{2}}$ m/s $^{2}$ towards N-W

Question 56: Palette 56/345

Allen MCQ

Starting from rest, the acceleration of a particle is $a = 2(t - 1) \, \text{m/s}^2$ . The velocity of the particle at t = 5 s is :-

A

15 m/s

B

25 m/s

C

5 m/s

D

None of these

Question 57: Palette 57/345

Allen MCQ

If the velocity of a particle is $(10 + 2t^{2})$ m/s, then the average acceleration of the particle between 2s and 5s is :-

A

$2m/s^{2}$

B

$4m/s^{2}$

C

$12m/s^{2}$

D

$14m/s^{2}$

Question 58: Palette 58/345

Allen MCQ

If velocity of a particle is given by $v = (3t^{2} + 2)m/s$ , then average velocity in the interval $0 \leq t \leq 2sec$ :

A

6 m/s

B

8 m/s

C

3 m/s

D

4 m/s

Question 59: Palette 59/345

Allen MCQ

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' which varies as $v = \alpha \sqrt{x}$ , then velocity of particle varies with time as: ( $\alpha$ is a constant)

A

$v \propto t$

B

$v \propto t^{2}$

C

$v \propto \sqrt{t}$

D

v = constant

Question 60: Palette 60/345

Allen MCQ

If the velocity of a particle is given by $v = (180 - 16x)^{1/2}$ m/s, then its acceleration will be:

A

Zero

B

$8 \, m/s^{2}$

C

$-8 \, m/s^{2}$

D

$4 \, m/s^{2}$

Question 61: Palette 61/345

Allen MCQ

The acceleration of a particle moving in a straight line varies with its displacement as $a = 2S + 1$ . Velocity of the particle is zero at zero displacement. The relation between velocity and displacement is :-

A

$v = S(S + 1)$

B

$v = \sqrt{2S(S + 1)}$

C

$v = \sqrt{S(S + 1)}$

D

None of these

Question 62: Palette 62/345

Allen MCQ

The position vector of a particle is given as $\vec{\mathrm{r}} = (t^2 - 4t + 6)\hat{\mathrm{i}} + (t^2)\hat{\mathrm{j}}$ . The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to:

A

1 sec.

B

2 sec.

C

1.5 sec.

D

5 sec.

Question 63: Palette 63/345

Allen MCQ

At any instant of time acceleration and velocity of a particle are given by $\vec{a} = \hat{i} + \hat{j}$ & $\vec{v} = 6\hat{i} + 8\hat{j}$ , then rate of change of speed (component of acceleration along velocity) at the same instant will be:-

A

$\frac{(3\hat{i} + 4\hat{j})}{25}$

B

$\frac{6\hat{i} + 8\hat{j}}{25}$

C

$\frac{7}{25}(3\hat{i} + 8\hat{j})$

D

$\frac{7}{25}(3\hat{i} + 4\hat{j})$

Question 64: Palette 64/345

Allen MCQ

If a body starts from rest, the time in which it covers a particular displacement with uniform acceleration is :

A

inversely proportional to the square root of the displacement

B

inversely proportional to the displacement

C

directly proportional to the displacement

D

directly proportional to the square root of the displacement

Question 65: Palette 65/345

Allen MCQ

A body at rest is imparted motion to move in a straight line. It is then obstructed by an opposite force, then:

A

the body may necessarily change direction

B

the body is sure to slow down

C

the body will necessarily continue to move in the same direction at the same speed

D

none of the above.

Question 66: Palette 66/345

Allen MCQ

If a car at rest accelerates uniformly to a speed of 144 km/h in 40 seconds, it covers a distance of :

A

200 m

B

800 m

C

1440 m

D

2980 m

Question 67: Palette 67/345

Allen MCQ

If a car at rest accelerates uniformly and attains a speed of 54 km/h in 10s, then it covers a distance of

A

75 m

B

100 m

C

200 m

D

400 m

Question 68: Palette 68/345

Allen MCQ

If a train travelling at 72 km/h is to be brought to rest in a distance of 100 m, then its retardation should be:

A

$20 \, m/s^{2}$

B

$2 \, m/s^{2}$

C

$10 \, m/s^{2}$

D

$1 \, m/s^{2}$

Question 69: Palette 69/345

Allen MCQ

Initially a body is at rest. If its acceleration is $5ms^{-2}$ then the distance travelled in the $5^{th}$ second is:-

A

86.6 m

B

87.5 m

C

88 m

D

22.5 m

Question 70: Palette 70/345

Allen MCQ

A car starts from rest travelling with constant acceleration. If distance covered by it in $10^{\text{th}}$ second of its journey is 19m, what will be the acceleration of car?

A

$4 \mathrm{~m} / \mathrm{s}^{2}$

B

$3 \mathrm{~m} / \mathrm{s}^{2}$

C

$2 \mathrm{~m} / \mathrm{s}^{2}$

D

$1 \mathrm{~m} / \mathrm{s}^{2}$

Question 71: Palette 71/345

Allen MCQ

A car starts from rest and moves with constant acceleration. The ratio of the distance covered in the $n^{th}$ second to that covered in n seconds is:

A

$\frac{2}{n^{2}} - \frac{1}{n}$

B

$\frac{2}{n^{2}} + \frac{1}{n}$

C

$\frac{2}{n} - \frac{1}{n^{2}}$

D

$\frac{2}{n} + \frac{1}{n^{2}}$

Question 72: Palette 72/345

Allen MCQ

A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 5th second?

A

$\frac{7}{5}$

B

$\frac{5}{7}$

C

$\frac{7}{9}$

D

$\frac{3}{7}$

Question 73: Palette 73/345

Allen MCQ

A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20m. If the velocity of the car is 40 m/s. It can be stopped by this force in:

A

$\frac{20}{3}$ m

B

320 m

C

60 m

D

180 m

Question 74: Palette 74/345

Allen MCQ

A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2m. If the same car is moving with a speed of 120 km/h., what is the minimum stopping distance?

A

2 m

B

4 m

C

6 m

D

18 m

Question 75: Palette 75/345

Allen MCQ

The velocity acquired by a body moving with uniform acceleration is 30 m/s in 2 seconds and 50 m/s in 4 seconds. The initial velocity is:

A

zero

B

2 m/s

C

4 m/s

D

10 m/s

Question 76: Palette 76/345

Allen MCQ

A body starts from rest and with a uniform acceleration of $5 \, ms^{-2}$ for 5 seconds. During the next 10 seconds it moves with uniform velocity. The total distance travelled by the body is:-

A

100 m

B

312.5 m

C

500 m

D

625 m

Question 77: Palette 77/345

Allen MCQ

The velocity of a particle moving with constant acceleration at an instant $t_{0}$ is 10 m/s. After 5 seconds of that instant the velocity of the particle is 20m/s. The velocity at 2 second before $t_{0}$ is:

A

8 m/s

B

4 m/s

C

6 m/s

D

7 m/s

Question 78: Palette 78/345

Allen MCQ

A bullet moving with a velocity of 200 cm/s penetrates a wooden block and comes to rest after traversing 4 cm inside it. What velocity is needed for travelling distance of 9 cm in same block :-

A

100 cm/s

B

136.2 cm/s

C

300 cm/s

D

250 cm/s

Question 79: Palette 79/345

Allen MCQ

Which of the following four statements is true?

A

A body can have zero velocity and still be accelerated

B

A body can have a constant velocity and still have a varying speed

C

A body cannot have a constant speed if it has a varying velocity

D

The direction of the velocity of a body cannot change when its acceleration is constant.

Question 80: Palette 80/345

Allen MCQ

If an iron ball and a wooden ball of same radii are released from a height h in vacuum then time taken by both of them to reach ground will be :

A

unequal

B

exactly equal

C

roughly equal

D

zero

Question 81: Palette 81/345

Allen MCQ

Three different objects of masses $m_{1}$ , $m_{2}$ and $m_{3}$ are allowed to fall from rest and from the same point '0' along three different frictionless paths. The speeds of the three objects on reaching the ground, will be in the ratio of:-

A

$m_{1}:m_{2}:m_{3}$

B

$m_{1}:2m_{2}:3m_{3}$

C

1:1:1

D

$\frac{1}{m_{1}}:\frac{1}{m_{2}}:\frac{1}{m_{3}}$

Question 82: Palette 82/345

Allen MCQ

A body dropped from a tower reaches the ground in 5s. The height of the tower is about:

A

80 m

B

125 m

C

160 m

D

40 m

Question 83: Palette 83/345

Allen MCQ

A stone falls freely such that the distance covered by it in the last second of its motion is equal to the distance covered by it in the first 3 seconds. It remained in air for:-

A

2 s

B

3 s

C

5 s

D

6 s

Question 84: Palette 84/345

Allen MCQ

A body dropped from the top of a tower covers 5x distance in the last second of its fall. The time of fall is if x is the distance covered in first second of its fall-

A

2 sec

B

4 sec.

C

3 sec.

D

$\left(\frac{50}{7}\right)$ sec

Question 85: Palette 85/345

Allen MCQ

An object is dropped vertically down on earth. The change in its speed after falling through a distance 2d from its highest point is

A

mgd

B

$\sqrt{2gd}$

C

$2\sqrt{gd}$

D

$2\sqrt{\frac{mg}{d}}$

Question 86: Palette 86/345

Allen MCQ

A bullet enters in a thick wooden wall with speed u. If the bullet penetrates a distance 's' into the wood then retardation of the bullet is:

A

$\frac{u^{2}}{s}$

B

$\frac{u^{2}}{2s}$

C

$\frac{u^{2}}{4s}$

D

$\frac{2u^{2}}{s}$

Question 87: Palette 87/345

Allen MCQ

A body dropped from the top of a tower covers a distance 9x in the last second of its journey, where x is the distance covered in first second. How much time does it take to reach the ground?

A

3s

B

4s

C

5s

D

6s

Question 88: Palette 88/345

Allen MCQ

A stone is dropped into a well in which the level of water is h below the top of the well. If v is velocity of sound, the time T after which the splash is heard is given by.

A

$T = \frac{2h}{v}$

B

$T = \sqrt{\frac{2h}{g}} + \frac{h}{v}$

C

$T = \sqrt{\frac{2h}{v}} + \frac{h}{g}$

D

$T = \sqrt{\frac{h}{2g}} + \frac{2h}{v}$

Question 89: Palette 89/345

Allen MCQ

A body is released from the top of a tower of height H metres. It takes t time to reach the ground. Where is the body $\frac{t}{3}$ time after the release:

A

At $\frac{H}{2}$ metres from ground

B

At $\frac{H}{4}$ metres from ground

C

At $\frac{8H}{9}$ metres from the ground

D

At $\frac{H}{9}$ metres from the ground

Question 90: Palette 90/345

Allen MCQ

A body falling from height 'h' takes $t_{1}$ time to reach the ground. The time taken to cover the first $\left(\frac{1}{4}\right)^{\text{th}}$ of the height is:

A

$t_{2} = \frac{t_{1}}{\sqrt{2}}$

B

$t_{1} = \frac{t_{2}}{\sqrt{2}}$

C

$t_{2} = \frac{t_{1}}{2}$

D

None of these

Question 91: Palette 91/345

Allen MCQ

A stone is dropped from a certain height which can reach the ground in 5 seconds. It is stopped after 3 seconds of its fall and is again released. The total time taken by the stone to reach the ground will be:

A

6 s

B

6.5 s

C

7 s

D

7.5 s

Question 92: Palette 92/345

Allen MCQ

A body released from a height falls freely towards earth. Another body is released from the same point exactly two second later. The separation between them two seconds after the release of the second body is:-

A

9.8 m

B

49 m

C

58.8 m

D

19.6 m

Question 93: Palette 93/345

Allen MCQ

Two balls are dropped from different heights at different instants. Second ball is dropped 2 seconds after the first ball. If both balls reach the ground simultaneously after 5 seconds of dropping the first ball, then the difference between the initial heights of the two balls will be: (g=9.8m/s $^{2}$ )

A

58.8 m

B

78.4 m

C

98.0 m

D

117.6 m

Question 94: Palette 94/345

Allen MCQ

A body is released from the top of a tower of height H m. After 2sec it is stopped and then instantaneously released. What will be its height from ground after next 2sec :-

A

(H-5) m

B

(H-10) m

C

(H-20)m

D

(H-40) m

Question 95: Palette 95/345

Allen MCQ

The ratio of the distances traversed, in successive intervals of time by a body falling from rest, are

A

1:3:5:7:9: .....

B

2:4:6:8:10: .....

C

1:4:7:10:13: .....

D

None of these

Question 96: Palette 96/345

Allen MCQ

A particle is dropped from a certain height. The time taken by it to fall through successive distances of 1 km each will be:

A

all equal, being equal to $\sqrt{\frac{2}{g}}$ second.

B

in the ratio of the square roots of the integers 1: $\sqrt{2}:\sqrt{3}$

C

in the ratio of the difference in the square roots of the integers, i.e., $\sqrt{1}, (\sqrt{2} - \sqrt{1}), (\sqrt{3} - \sqrt{2}), (\sqrt{4} - \sqrt{3})$ .....

D

in the ratio of the reciprocals of the square roots of the integers, ie., $\frac{1}{\sqrt{1}}$ , $\frac{1}{\sqrt{2}}$ , $\frac{1}{\sqrt{3}}$ .....

Question 97: Palette 97/345

Allen MCQ

Drops of water fall from the roof of a building 27m high at regular intervals of time. When the first drop reaches the ground, at the same instant fourth drop begins to fall. What are the distances of the second and third drops from the roof?

A

6 m and 12 m

B

6 m and 3 m

C

12 m and 3 m

D

8 m and 2 m

Question 98: Palette 98/345

Allen MCQ

Water drops fall at regular intervals from a tap 6 m above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant?

A

1.25 m

B

2.50 m

C

3.75 m

D

4.5 m

Question 99: Palette 99/345

Allen MCQ

Four marbles are dropped from the top of a tower one after the other with an interval of one second. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third and the third and forth will be respectively:

A

$35\mathrm{m}$ , $25\mathrm{m}$ and $15\mathrm{m}$

B

$30\mathrm{m}$ , $20\mathrm{m}$ and $10\mathrm{m}$

C

$20\mathrm{m}$ , $10\mathrm{m}$ and $5\mathrm{m}$

D

$40\mathrm{m}$ , $30\mathrm{m}$ and $20\mathrm{m}$

Question 100: Palette 100/345

Allen MCQ

A particle is thrown vertically upward. Its velocity at half of the maximum height is 10m/s. The maximum height attained by it is (g=10 ms $^{-2}$ ):-

A

8m

B

20m

C

10m

D

16m

Question 101: Palette 101/345

Allen MCQ

A ball is thrown upward with a velocity of 50 m/s. It will reach the ground after:-

A

10 s

B

20 s

C

5 s

D

40 s

Question 102: Palette 102/345

Allen MCQ

Two bodies are thrown vertically upwards with their initial speeds in the ratio 2:3. The ratio of the maximum heights reached by them and the ratio of time taken by them to return back to the ground respectively are:

A

$4:9$ and $2:3$

B

$2:3$ and $\sqrt{2}:\sqrt{3}$

C

$\sqrt{2}:\sqrt{3}$ and $4:9$

D

$\sqrt{2}:\sqrt{3}$ and $2:3$

Question 103: Palette 103/345

Allen MCQ

A particle is thrown from the ground upward with velocity 40 m/s. Calculate maximum height:-

A

40 m

B

80 m

C

160 m

D

8 m

Question 104: Palette 104/345

Allen MCQ

If a ball is thrown vertically upwards with 40 m/s, its velocity after three seconds will be:

A

10 m/s

B

20 m/s

C

30 m/s

D

40 m/s

Question 105: Palette 105/345

Allen MCQ

When a ball is thrown vertically up with velocity $v_{0}$ , it reaches a maximum height 'h'. If one wishes to double the maximum height then the ball should be thrown with velocity -

A

$\sqrt{2}v_{0}$

B

$3v_{0}$

C

$9v_{0}$

D

$3/2v_{0}$

Question 106: Palette 106/345

Allen MCQ

With what speed should a body be thrown upwards so that the distances traversed in 7th second and 8th second are equal?

A

58.4 m/s

B

49 m/s

C

$\sqrt{98}$ m/s

D

68.6 m/s

Question 107: Palette 107/345

Allen MCQ

If a ball is thrown vertically upwards with speed u, the distance covered during the last 't' seconds of its ascent is :-

A

ut

B

$\frac{1}{2} \mathrm{gt}^2$

C

$\mathrm{ut} - \frac{1}{2} \mathrm{gt}^2$

D

$(\mathrm{u} + \mathrm{gt}) \mathrm{t}$

Question 108: Palette 108/345

Allen MCQ

A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distance travelled by the body in the first second and the seventh second is:-

A

$1:1$

B

$11:1$

C

$1:2$

D

$5:3$

Question 109: Palette 109/345

Allen MCQ

A ball is thrown vertically upwards with velocity 600 m/s. Calculate distance travelled in last 2 sec of its upward motion :-

A

20 m

B

30 m

C

10 m

D

25 m

Question 110: Palette 110/345

Allen MCQ

A body is projected vertically up at t = 0 with a velocity of 98 m/s. Another body is projected from the same point with same velocity after 4 seconds. Both bodies will meet at t =

A

6 s

B

8 s

C

10 s

D

12 s

Question 111: Palette 111/345

Allen MCQ

A ball is thrown vertically upwards. The ball was observed at a height h twice with a time interval $\Delta t$ . The initial velocity of the ball is

A

$\sqrt{8gh + (g\Delta t)^{2}}$

B

$\sqrt{2gh + \left(\frac{g\Delta t}{2}\right)^{2}}$

C

$\sqrt{8gh + (2g\Delta t)^{2}}$

D

$\sqrt{2gh}$

Question 112: Palette 112/345

Allen MCQ

A ball is thrown vertically upwards. Assuming the air resistance to be constant and considerable :-

A

the time of ascent $\geq$ the time of descent

B

the time of ascent $<$ the time of descent

C

the time of ascent $>$ the time of descent

D

the time of ascent $=$ the time of descent

Question 113: Palette 113/345

Allen MCQ

A particle is thrown up vertically with a speed 'v₁', in air. It takes time t₁ in upward journey and t₂ (> t₁) in the downward journey and returns to the starting point with a speed v₂. Then:

A

$v_{1} = v_{2}$

B

$v_{1} < v_{2}$

C

$v_{1} > v_{2}$

D

Data is insufficient

Question 114: Palette 114/345

Allen MCQ

A particle is thrown upwards from ground. It experiences a constant resistance force which produces a retardation of $2\mathrm{m} / \mathrm{s}^2$ . The ratio of time of ascent to the time of descent is $(\mathrm{g} = 10\mathrm{m} / \mathrm{s}^2)$ :-

A

1

B

$\sqrt{\frac{2}{3}}$

C

$\frac{2}{3}$

D

$\sqrt{\frac{3}{2}}$

Question 115: Palette 115/345

Allen MCQ

A stone is thrown straight upward with a speed of 20 m/sec from a tower 200 m high. The speed with which it strikes the ground is approximately $(g = 9.8 \, \text{m/s}^2)$

A

60 m/sec

B

65 m/sec

C

70 m/sec

D

75 m/sec

Question 116: Palette 116/345

Allen MCQ

A balloon is at a height of 81 m and is ascending upwards with a velocity of 12 m/s. A body of 2 kg weight is dropped from it. If g = 10 m/s $^{2}$ , the body will reach the surface of the earth in:

A

1.5 s

B

4.025 s

C

5.4 s

D

6.75 s

Question 117: Palette 117/345

Allen MCQ

A ball is thrown vertically upwards from the top of a tower with velocity $4.9 \, ms^{-1}$ . It strikes the pond near the base of the tower after 3 seconds. The height of the tower is :-

A

73.5 m

B

44.1 m

C

29.4 m

D

None of these

Question 118: Palette 118/345

Allen MCQ

A stone is thrown upwards with a speed 'u' from the top of the tower reaches the ground with a velocity '3u'. The height of the tower is:-

A

$\frac{3\mathrm{u}^2}{\mathrm{g}}$

B

$\frac{4\mathrm{u}^2}{\mathrm{g}}$

C

$\frac{6\mathrm{u}^2}{\mathrm{g}}$

D

$\frac{9\mathrm{u}^2}{\mathrm{g}}$

Question 119: Palette 119/345

Allen MCQ

A body dropped from a height h, strikes the ground with velocity 3 m/s. Another body of same mass is thrown downward from the height h with an initial velocity of 4 m/s. Find the final velocity with which it strikes the ground

A

3 m/s

B

4 m/s

C

5 m/s

D

12 m/s

Question 120: Palette 120/345

Allen MCQ

From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically) with same speed. If $V_{A}$ and $V_{B}$ are their respective velocities on reaching the ground then:

A

$V_{B} > V_{A}$

B

$V_{A} = V_{B}$

C

$V_{A} > V_{B}$

D

None of these

Question 121: Palette 121/345

Allen MCQ

A stone falls from a balloon that is descending at a uniform rate of $10 \, ms^{-1}$ . The displacement of the stone from the point of release after 10 seconds is: $(g = 10 \, \text{m/s}^2)$

A

490 m

B

510 m

C

600 m

D

725 m

Question 122: Palette 122/345

Allen MCQ

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at $2 \, m/s^{2}$ . He reaches the ground with a speed of 3 m/s. At what approximate height, did he bail out?

A

293 m

B

111 m

C

91 m

D

182 m

Question 123: Palette 123/345

Allen MCQ

A rocket is fired vertically from the ground. It moves upwards with a constant acceleration $20 \, m/s^{2}$ for 30 sec after which the fuel is finished. After what time from the instant of firing the rocket will attain the maximum height? (Take $g = 10 \, m/s^{2}$ )

A

90 s

B

45 s

C

60 s

D

75 s

Question 124: Palette 124/345

Allen MCQ

The velocity-time graph of an object is shown. The distance during the interval 0 to $t_4$ is :-

A

Area A + Area B + Area C + Area D + Area E

B

Area A + Area C - Area B - Area D

C

Area A + Area B + Area C + Area D

D

Area A + Area C + Area E - Area B + Area D

Question 125: Palette 125/345

Allen MCQ

Figure below shows the acceleration-time graph of a one dimensional motion. Which of the following characteristics of the particle is represented by the shaded area?

A

change in velocity

B

change in position

C

change in momentum

D

velocity

Question 126: Palette 126/345

Allen MCQ

Fig. shows the displacement of a particle moving along x-axis as a function of time. The velocity of the particle is zero at :-

A

A

B

B

C

C

D

D

Question 127: Palette 127/345

Allen MCQ

The displacement-time graph of a moving particle is shown. The instantaneous velocity of the particle is positive at the point :

A

D

B

F

C

C

D

E

Question 128: Palette 128/345

Allen MCQ

A person walks along an east-west street and a graph of his displacement from home is shown in figure. His average speed for the whole time interval is

A

0

B

23 m/s

C

8 m/s

D

None of these

Question 129: Palette 129/345

Allen MCQ

A particle is moving in a straight line y=3x. Its velocity time graph is shown in figure. Its speed is minimum at t=.....

A

2s

B

4s

C

6s

D

8s

Question 130: Palette 130/345

Allen MCQ

The displacement-time graph for two particles A and B are straight lines inclined at angles of $30^{\circ}$ and $60^{\circ}$ with the time axis. The ratio of velocity of particle A & B ( $V_{A}:V_{B}$ ) is :-

A

$1:2$

B

$1:\sqrt{3}$

C

$\sqrt{3}:1$

D

$1:3$

Question 131: Palette 131/345

Allen MCQ

Which one of the following curves do not represent motion in one dimension :-

A

B

C

D

Question 132: Palette 132/345

Allen MCQ

Which of the following displacement-time graphs shows a realistic situation for a body in motion?

A

B

C

D

Question 133: Palette 133/345

Allen MCQ

Which of the following velocity-time graphs represent uniformly accelerated motion?

A

B

C

D

Question 134: Palette 134/345

Allen MCQ

The fig. shows the position time graph of a particle moving on a straight line path. What is the magnitude of average speed of the particle over 10 seconds?

A

2 m/s

B

4 m/s

C

6 m/s

D

8 m/s

Question 135: Palette 135/345

Allen MCQ

From the following velocity time graph of a body the distance travelled by the body and its displacement during 5 seconds in metres will be :

A

75, 75

B

110, 70

C

110, 110

D

110, 40

Question 136: Palette 136/345

Allen MCQ

The v-t graph of linear motion of a particle starts its motion from origin is shown in adjoining figure. The distance of particle from origin after 8 sec. is :-

A

18 meters

B

16 meters

C

8 meters

D

6 meters

Question 137: Palette 137/345

Allen MCQ

A particle moves according to given velocity-time graph. Then the ratio of distance travelled in last 4 seconds and 9 seconds is :-

A

$\frac{1}{4}$

B

$\frac{2}{5}$

C

$\frac{1}{8}$

D

$\frac{4}{11}$

Question 138: Palette 138/345

Allen MCQ

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in 6 s are, respectively :-

A

8 m, 16 m

B

$16 \mathrm{~m}, 8 \mathrm{~m}$

C

16 m, 16 m

D

$8 \mathrm{~m}, 8 \mathrm{~m}$

Question 139: Palette 139/345

Allen MCQ

The variation of velocity of a particle moving along a straight line is illustrated in the figure. The distance transversed by the particle in 3 seconds is

A

60 m

B

45 m

C

55 m

D

30 m

Question 140: Palette 140/345

Allen MCQ

Velocity-time (v-t) graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is zero acceleration is:-

A

60 m

B

50 m

C

30 m

D

40 m

Question 141: Palette 141/345

Allen MCQ

The velocity versus time curve of a moving particle is as shown in the following figure. The maximum acceleration is

A

$$<br /> 1 \mathrm{m} \sec^ {- 2}<br /> $$

B

$$<br /> 2 \mathrm{m} \sec^ {- 2}<br /> $$

C

$$<br /> 3\mathrm{m} \sec^ {- 2}<br /> $$

D

$$<br /> 4\sec^ {- 2}<br /> $$

Question 142: Palette 142/345

Allen MCQ

Find the average acceleration of the block from time t=2 sec to t=4 sec.

A

$5\mathrm{m / s^2}$

B

$10\mathrm{m / s^2}$

C

$-5\mathrm{m / s^2}$

D

$-10\mathrm{m / s^2}$

Question 143: Palette 143/345

Allen MCQ

A particle starts from rest. Its acceleration at time t = 0 is $5 \, m/s^{2}$ which varies with time as shown in the figure. The maximum speed of the particle will be :

A

$7.5\mathrm{m / s}$

B

$15\mathrm{m / s}$

C

$20\mathrm{m / s}$

D

$37.5\mathrm{m / s}$

Question 144: Palette 144/345

Allen MCQ

A particle starts from rest, its acceleration-time graph is shown in figure. Find out velocity at t = 4 sec

A

20 m/s

B

30 m/s

C

40 m/s

D

None of these

Question 145: Palette 145/345

Allen MCQ

Which of the following options is correct for the object having a straight line motion represented by the following graph :-

A

The object moves with constantly increasing velocity from O to A and then it moves with constant velocity.

B

Velocity of the object increases uniformly

C

Average velocity is zero

D

The graph shown is impossible

Question 146: Palette 146/345

Allen MCQ

For the motion of a particle acceleration-time graph is shown in figure. The velocity time curve for the duration of 0 - 4 seconds is :

A

B

C

D

Question 147: Palette 147/345

Allen MCQ

Acceleration-time graph of a body initially at rest is shown. The corresponding velocity-time graph of the same body is :-

A

B

C

D

Question 148: Palette 148/345

Allen MCQ

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement :-

A

B

C

D

Question 149: Palette 149/345

Allen MCQ

The x - t graph of a particle moving along a straight line is shown in figure. The distance-time graph of the particle is correctly shown by :

A

B

C

D

Question 150: Palette 150/345

Allen MCQ

A particle starts from rest and move with constant acceleration. Its velocity-displacement curve is :

A

B

C

D

Question 151: Palette 151/345

Allen MCQ

Acceleration-time curve for a body projected vertically upwards is a/an :-

A

Parabola

B

Ellipse

C

Hyperbola

D

Straight line

Question 152: Palette 152/345

Allen MCQ

A body is projected vertically upward from the surface of the earth, its displacement-time graph is :

A

B

C

D

Question 153: Palette 153/345

Allen MCQ

A rocket is launched upward from the earth's surface whose velocity time graphs shown in figure. Then maximum height attained by the rocket is:

A

$1\mathrm{km}$

B

$10\mathrm{km}$

C

$100\mathrm{km}$

D

$60\mathrm{km}$

Question 154: Palette 154/345

Allen MCQ

A rocket is launched upward from the earth's surface whose velocity time graphs shown in figure. Then maximum height attained by the rocket is: , height covered by the rocket before retardation is:

A

1 km

B

10 km

C

20 km

D

60 km

Question 155: Palette 155/345

Allen MCQ

A rocket is launched upward from the earth's surface whose velocity time graphs shown in figure. Then maximum height attained by the rocket is: , mean velocity of rocket during the time it took to attain the maximum height:

A

100 m/s

B

50 m/s

C

500 m/s

D

25/3 m/s

Question 156: Palette 156/345

Allen MCQ

A rocket is launched upward from the earth's surface whose velocity time graphs shown in figure. Then maximum height attained by the rocket is: , the retardation of rocket is:

A

$50 \, m/s^{2}$

B

$100 \, m/s^{2}$

C

$500 \, m/s^{2}$

D

$10 \, m/s^{2}$

Question 157: Palette 157/345

Allen MCQ

A rocket is launched upward from the earth's surface whose velocity time graphs shown in figure. Then maximum height attained by the rocket is: , the acceleration of rocket is:

A

$50 \, m/s^{2}$

B

$100 \, m/s^{2}$

C

$10 \, m/s^{2}$

D

$1000 \, m/s^{2}$

Question 158: Palette 158/345

Allen MCQ

A rocket is launched upward from the earth's surface whose velocity time graphs shown in figure. Then maximum height attained by the rocket is: , the rocket goes up and comes down on the following parts respectively:

A

OA and AB

B

AB and BC

C

OA and ABC

D

OAB and BC

Question 159: Palette 159/345

Allen MCQ

A ball is dropped from the certain height on the surface of glass. It collides elastically and comes back to its initial position. If this process it repeated then the velocity time graph is : (Take downward direction as positive)

A

B

C

D

Question 160: Palette 160/345

Allen MCQ

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistance, The graph according to which its velocity V varies with the height h above the ground is :-

A

B

C

D

Question 161: Palette 161/345

Allen MCQ

A stone is thrown upwards from top of a tower 60 m high at a speed of 20 m/s. The correct position-time graph for the time interval in which it reaches ground, is (g = 10 m/s $^{2}$ & take origin at the base of the tower):

A

B

C

D

Question 162: Palette 162/345

Allen MCQ

A car starts from rest and accelerates uniformly by for 4 seconds and then moves with uniform velocity which of the x-t graph represent the motion of the car?

A

B

C

D

Question 163: Palette 163/345

Allen MCQ

Figure shows x-t graph of a particle. Find the time t such that the average velocity of the particle during the period 0 to t is zero

A

6 sec.

B

8 sec.

C

10 sec.

D

12 sec.

Question 164: Palette 164/345

Allen MCQ

Graph between the square of the velocity (v) of a particle and the distance (s) moved is shown in figure. The acceleration of the particle in kilometers per hour square is :

A

2250

B

3084

C

– 2250

D

– 3084

Question 165: Palette 165/345

Allen MCQ

A train takes 4 min. to go between stations 2.25 km apart starting and finishing at rest. The acceleration is uniform for the first 40 sec and the deceleration is uniform for the last 20 sec. Assuming the velocity to be constant for the remaining time, then maximum speed of the train is :-

A

75 m/sec

B

18.75 m/sec

C

37.5 m/sec

D

10.7 m/sec

Question 166: Palette 166/345

Allen MCQ

A car accelerates from rest at a constant rate of $2 \, m/s^{2}$ for some time. Then, it retards at a constant rate of $4 \, m/s^{2}$ and comes to rest. If it remains in motion for 3 seconds, then the maximum speed attained by the car is:

A

2 m/s

B

3 m/s

C

4 m/s

D

6 m/s

Question 167: Palette 167/345

Allen MCQ

In the graph shown in fig. time is plotted along x-axis. Which quantity associated with a projectile motion is plotted along the y-axis?

A

kinetic energy

B

momentum

C

horizontal velocity

D

none of the above

Question 168: Palette 168/345

Allen MCQ

For ground to ground projection following curves are given :-
(a)

(b)

(c)

(d)

Find incorrect one.

A

a

B

b

C

c

D

d

Question 169: Palette 169/345

Allen MCQ

If air resistance is not considered in projectile motion, the horizontal motion takes place with

A

constant velocity

B

constant acceleration

C

constant retardation

D

variable velocity

Question 170: Palette 170/345

Allen MCQ

In a projectile motion, the velocity:-

A

is always perpendicular to the acceleration

B

is never perpendicular to the acceleration

C

is perpendicular to the acceleration for one instant only

D

is perpendicular to the acceleration for two instants

Question 171: Palette 171/345

Allen MCQ

In projectile motion, the modulus of rate of change of velocity-

A

is constant

B

first increases then decreases

C

first decreases then increases

D

None of the above

Question 172: Palette 172/345

Allen MCQ

Which of the following quantities remains constant during projectile motion?
(A) Average velocity between two points.
(B) Average speed between two points
(C) $\frac{d\vec{v}}{dt}$ (D) $\frac{d^{2}}{dt^{2}}(\vec{v})$

A

only A

B

only C

C

A and C

D

C and D

Question 173: Palette 173/345

Allen MCQ

A bomb is fired from a cannon with a velocity of 1000 m/s making an angle of $30^{\circ}$ with the horizontal. What is the time taken by the bomb to reach at the highest point-

A

11 sec

B

23 sec

C

38 sec

D

50 sec

Question 174: Palette 174/345

Allen MCQ

If time of flight of a projectile is 10 seconds. Range is 500 meters. The maximum height attained by it will be :-

A

125 m

B

50 m

C

100 m

D

150 m

Question 175: Palette 175/345

Allen MCQ

A body is thrown with a velocity of 19.6 m/s making an angle of $30^{\circ}$ with the horizontal. It will hit the ground after a time:—

A

3 s

B

2 s

C

1.5 s

D

1 s

Question 176: Palette 176/345

Allen MCQ

If a projectile is fired at an angle $\theta$ to the vertical with velocity $u$ , then maximum height attained is given by:

A

$\frac{u^2 \cos \theta}{2g}$

B

$\frac{u^2 \sin^2 \theta}{2g}$

C

$\frac{u^2 \sin^2 \theta}{g}$

D

$\frac{u^2 \cos^2 \theta}{2g}$

Question 177: Palette 177/345

Allen MCQ

At the uppermost point of a projectile its velocity and acceleration are at an angle of:-

A

$180^{\circ}$

B

$90^{\circ}$

C

$60^{\circ}$

D

$45^{\circ}$

Question 178: Palette 178/345

Allen MCQ

Two projectiles are projected with velocity $v_{A}$ , $v_{B}$ at angles $\theta_{A}$ (from horizontal) and $\theta_{B}$ (from vertical) as shown in the figure below, such that $v_{A} > v_{B}$ but having same horizontal component of velocity. Which of the following can not be correct?

A

$\mathrm{T_A > T_B}$

B

$\mathrm{H_A > H_B}$

C

$\mathrm{R_A > R_B}$

D

$\mathrm{R_B > R_A}$

Question 179: Palette 179/345

Allen MCQ

A player throws a ball that reaches to the another player in 4s. If the height of each player is 1.5m, the maximum height attained by the ball from the ground level is:

A

19.6 m

B

21.1 m

C

23.6 m

D

25.1 m

Question 180: Palette 180/345

Allen MCQ

A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with speed v. While rising up the magnitude of the velocity after t seconds will be:

A

$\sqrt{(v\cos\theta)^2 + (v\sin\theta)^2}$

B

$\sqrt{(v\cos\theta - v\sin\theta)^2 - gt}$

C

$\sqrt{v^2 + g^2t^2 - (2v\sin\theta)gt}$

D

$\sqrt{v^2 + g^2t^2 - (2v\cos\theta)gt}$

Question 181: Palette 181/345

Allen MCQ

A particle is fired with velocity u making $\theta$ angle with the horizontal. What is the magnitude of change in velocity when it returns to the ground.

A

u cos $\theta$

B

u

C

2u sin $\theta$

D

(u cos $\theta - u$ )

Question 182: Palette 182/345

Allen MCQ

In the above, the change in speed is:

A

u cos θ

B

0

C

u sin θ

D

(u cosθ - u)

Question 183: Palette 183/345

Allen MCQ

The angle which the velocity vector of a projectile, will make with the vertical after time t of its being thrown with a velocity v at an angle $\theta$ to the horizontal, is:

A

$\theta$

B

$\tan^{-1}\left(\frac{\theta}{t}\right)$

C

$\tan^{-1}\left(\frac{v\cos\theta}{v\sin\theta-gt}\right)$

D

$\tan^{-1}\left(\frac{v\sin\theta-gt}{v\cos\theta}\right)$

Question 184: Palette 184/345

Allen MCQ

At a height 0.4 m from the ground, the velocity of a projectile in vector form is: $\vec{v}=(6\hat{i}+2\hat{j})$ m/s. The angle of projection from horizontal is $(g=10\mathrm{~m/s^{2}})$:-

A

$45^{\circ}$

B

$60^{\circ}$

C

$30^{\circ}$

D

$\tan^{-1}(3/4)$

Question 185: Palette 185/345

Allen MCQ

In case of a projectile fired at an angle $60^{\circ}$ to the horizontal with velocity u, the horizontal range is:

A

$\frac{u^{2}}{g}$

B

$\frac{\sqrt{3}u^{2}}{2g}$

C

$\frac{2u^{2}}{g}$

D

$\frac{u^{2}}{g^{2}}$

Question 186: Palette 186/345

Allen MCQ

If the instantaneous velocity of a particle projected as shown in figure is given by $\vec{v}=a\hat{i}+(b-ct)\hat{j}$ where a, b and c are positive constants, the range on the horizontal plane will be :

A

2ab/c

B

ab/c

C

ac/b

D

a/2bc

Question 187: Palette 187/345

Allen MCQ

A projectile is thrown from a point in a horizontal plane such that its horizontal and vertical velocity components are 9.8 m/s and 4.9 m/s respectively. Its horizontal range is:

A

4.9 m

B

9.8 m

C

19.6 m

D

39.2 m

Question 188: Palette 188/345

Allen MCQ

A projectile is projected with initial velocity $(5\hat{i}+12\hat{j})$ m/s. If g = 10 ms $^{-2}$ , then horizontal range is :

A

4.8 metre

B

9.6 metre

C

19.2 metre

D

12 metre

Question 189: Palette 189/345

Allen MCQ

A shell is fired vertically upwards with a velocity $v_{1}$ from the deck of a ship moving with a speed $v_{2}$ . A person on the shore observes the motion of the shell as a parabola. Its horizontal range is given by:

A

$\frac{2v_{1}^{2}v_{2}}{g}$

B

$\frac{2v_{1}v_{2}^{2}}{g}$

C

$\frac{2v_{1}v_{2}}{g}$

D

$\frac{2v_{1}^{2}v_{2}^{2}}{g}$

Question 190: Palette 190/345

Allen MCQ

The range of a projectile when fired at $60^{\circ}$ to the horizontal is 0.5 km. What will be its range when fired at $45^{\circ}$ with the same speed?

A

0.5 km

B

$\frac{1.0}{\sqrt{3}}$ km

C

1.5 km

D

2.0 km

Question 191: Palette 191/345

Allen MCQ

The speed of a projectile at its maximum height is $\frac{1}{2}$ times of its initial speed 'u' of projection. Its range on the horizontal plane is:

A

$\frac{\sqrt{3}u^2}{2g}$

B

$\frac{u^2}{2g}$

C

$\frac{3u^2}{2g}$

D

$\frac{3u^2}{g}$

Question 192: Palette 192/345

Allen MCQ

A bullet is fired from a cannon with velocity 500 m/s. If the angle of projection is $15^{\circ}$ and $g = 10m/s^{2}$ . Then the range is :-

A

$25 \times 10^{3}$ m

B

$12.5 \times 10^{3}$ m

C

$50 \times 10^{2}$ m

D

$25 \times 10^{2}$ m

Question 193: Palette 193/345

Allen MCQ

For a given angle of projection if the initial velocity is tripled the range of the projectile becomes :-

A

9 times

B

one-fourth

C

two times

D

four times

Question 194: Palette 194/345

Allen MCQ

A ball is thrown at an angle $\theta$ to the vertical and the range is maximum. The value of $\tan\theta$ is:

A

1

B

$\sqrt{3}$

C

$\frac{1}{\sqrt{3}}$

D

2

Question 195: Palette 195/345

Allen MCQ

The maximum horizontal range of a gun is 25 km. If g = 10 m/s $^{2}$ , the muzzle velocity of the shell must be:-

A

1600 m/s

B

500 m/s

C

200 $\sqrt{2}$ m/s

D

160 $\sqrt{10}$ m/s

Question 196: Palette 196/345

Allen MCQ

A grasshopper can jump maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10 seconds:-

A

$5\sqrt{2}\mathrm{m}$

B

$10\sqrt{2}\mathrm{m}$

C

$20\sqrt{2}\mathrm{m}$

D

$40\sqrt{2}\mathrm{m}$

Question 197: Palette 197/345

Allen MCQ

Three projectiles A, B and C are thrown from the same point in the same plane. Their trajectories are shown in the figure. Which of the following statement is incorrect?

A

The time of flight is the same for all the three

B

The launch speed is same for all the three

C

The horizontal velocity component is largest for particle C

D

The maximum height is same for all the three

Question 198: Palette 198/345

Allen MCQ

A projectile is thrown with an initial velocity of $\vec{v} = a\hat{i} + b\hat{j}$ . If range of the projectile is four times the maximum height attained by it then:

A

$a = 2b$

B

$b = a$

C

$b = 2a$

D

$b = 4a$

Question 199: Palette 199/345

Allen MCQ

Two projectiles are fired from the same point with the same speeds at angles of projection $60^{\circ}$ and $30^{\circ}$ respectively. Which one of the following is true?

A

Their horizontal ranges will be the same

B

Their maximum heights will be the same

C

Their landing velocities will be the same

D

Their times of flight will be the same

Question 200: Palette 200/345

Allen MCQ

Three particles A, B and C are projected from the same point with the same initial speeds making angles $30^{\circ}$ , $45^{\circ}$ and $60^{\circ}$ respectively with the horizontal. Which of the following statements are correct?

A

A, B and C have unequal ranges

B

Ranges of A and C are equal and less than that of B

C

Ranges of A and C are equal and greater than that of B

D

A, B and C have equal ranges

Question 201: Palette 201/345

Allen MCQ

A number of bullets are fired in all possible directions with the same initial velocity u. The maximum area of ground covered by bullets is:-

A

$\pi\left(\frac{2u^{2}}{g}\right)^{2}$

B

$3\pi\left(\frac{u}{g}\right)^{2}$

C

$5\pi\left(\frac{u}{2g}\right)^{2}$

D

$\pi\left(\frac{u^{2}}{g}\right)^{2}$

Question 202: Palette 202/345

Allen MCQ

Four bodies P, Q, R and S are projected with equal speed having angles of projection $15^{\circ}$ , $30^{\circ}$ , $45^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The body having shortest range is:

A

P

B

Q

C

R

D

S

Question 203: Palette 203/345

Allen MCQ

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance up to which the boy can throw the same stone will be :

A

$20\sqrt{2}$ m

B

10 m

C

$10\sqrt{2}$ m

D

20 m

Question 204: Palette 204/345

Allen MCQ

A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball :-

A

200m

B

400m

C

100m

D

50m

Question 205: Palette 205/345

Allen MCQ

The cannon was set by mistake at $30^{\circ}$ instead of $20^{\circ}$ with the horizontal and was fired to hit the enemy target. The cannon-shell will now fall at :

A

The enemy target

B

Before the enemy target

C

Beyond the enemy target

D

May fall at any place

Question 206: Palette 206/345

Allen MCQ

Two similar cannon simultaneously fires two identical cannon balls at target 1 and 2 as shown in the figure. If the cannon balls have identical initial speeds, which of the following statements is true?

A

Target 2 is hit before target 1

B

Target 1 is hit before target 2

C

Both are hit at the same time

D

information is insufficient

Question 207: Palette 207/345

Allen MCQ

If R is the horizontal range of a particle projected at an angle $53^{\circ}$ from horizontal, then the greatest height attained by it is:

A

$\frac{R}{3}$

B

2R

C

$\frac{R}{2}$

D

$\frac{R}{4}$

Question 208: Palette 208/345

Allen MCQ

A projectile can have the same range R for two angles of projection. If $h_{1}$ and $h_{2}$ be the maximum height in the two cases, then:

A

$h_{1}h_{2} \propto R^{2}$

B

$h_{1}h_{2} \propto R$

C

$h_{1}h_{2} \propto \frac{1}{R}$

D

$h_{1}h_{2} \propto \frac{1}{R^{2}}$

Question 209: Palette 209/345

Allen MCQ

A body is thrown with some velocity from the ground. Maximum height attained when it is thrown at $37^{\circ}$ to the horizontal is 90 m. What is the height attained when it is thrown at $53^{\circ}$ to the horizontal?

A

90 m

B

45 m

C

120 m

D

160 m

Question 210: Palette 210/345

Allen MCQ

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\frac{\pi}{6}$ and its maximum height is $y_{1}$ , then the maximum height of the other will be:

A

$3y_{1}$

B

$2y_{1}$

C

$\frac{y_{1}}{2}$

D

$\frac{y_{1}}{3}$

Question 211: Palette 211/345

Allen MCQ

A ball is thrown at different angles with the same speed u and from the same point; it has the same range in both the cases. If $y_{1}$ and $y_{2}$ be the heights attained in the two cases, then $y_{1} + y_{2} = \ldots$ :

A

$\frac{u^{2}}{g}$

B

$\frac{2u^{2}}{g}$

C

$\frac{u^{2}}{2g}$

D

$\frac{u^{2}}{4g}$

Question 212: Palette 212/345

Allen MCQ

A body is projected at such an angle that the horizontal range is four times the greatest height. The angle of projection is:-

A

$25^{\circ}$

B

$33^{\circ}$

C

$45^{\circ}$

D

$53^{\circ}$

Question 213: Palette 213/345

Allen MCQ

The horizontal range of a projectile is $4\sqrt{3}$ times of its maximum height. Its angle of projection from horizontal will be:

A

$45^{\circ}$

B

$60^{\circ}$

C

$90^{\circ}$

D

$30^{\circ}$

Question 214: Palette 214/345

Allen MCQ

A projectile have range double as compare to its maximum height attained. The angle of projection from horizontal is-

A

$\tan^{-1}(2)$

B

$\tan^{-1}(4)$

C

$\tan^{-1}(3)$

D

$\tan^{-1}(5)$

Question 215: Palette 215/345

Allen MCQ

The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times its initial speed. If the range of the projectile is 'P' times the maximum height attained by it, then P equals to -

A

$\frac{4}{3}$

B

$2\sqrt{3}$

C

$4\sqrt{3}$

D

$\frac{3}{4}$

Question 216: Palette 216/345

Allen MCQ

A ball is projected to attain the maximum range. If the height attained is H, the range is

A

H

B

2H

C

4H

D

H/2

Question 217: Palette 217/345

Allen MCQ

The equation of a projectile is $y = x - \frac{gx^2}{2}$ . The angle of projection is:

A

30°

B

60°

C

45°

D

none

Question 218: Palette 218/345

Allen MCQ

The equation of a projectile is $y = 4x - \frac{x^{2}}{4}$ . The horizontal range is:

A

16 m

B

8 m

C

64 m

D

12.8 m

Question 219: Palette 219/345

Allen MCQ

A particle is projected at an angle of $45^{\circ}$ from horizontal, 6m away from the foot of a wall, just touches the top of the wall and falls on the ground on the opposite side at a distance 3m from it. The height of wall is:

A

2m

B

$\frac{4}{3}$ m

C

$\frac{8}{3}$ m

D

$\frac{3}{4}$ m

Question 220: Palette 220/345

Allen MCQ

A stone is projected from the ground with velocity 50 m/s at an angle of $30^{\circ}$ from horizontal. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground (g = 10m/sec $^{2}$ )

A

90.2 m

B

89.6 m

C

86.6 m

D

70.2 m

Question 221: Palette 221/345

Allen MCQ

A shell fired from the ground is just able to cross the top of a wall 90m away and 45 m high moving horizontally. The direction of projection of the shell from horizontal will be :-

A

$25^{\circ}$

B

$30^{\circ}$

C

$60^{\circ}$

D

$45^{\circ}$

Question 222: Palette 222/345

Allen MCQ

An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , then the horizontal component of the velocity of arrow is:

A

40 m/s

B

20 m/s

C

31.25 m/s

D

12.5 m/s

Question 223: Palette 223/345

Allen MCQ

An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the maximum height attained by the arrow is:

A

25 m

B

20 m/s

C

31.25 m

D

12.5 m

Question 224: Palette 224/345

Allen MCQ

An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the vertical component of the projection velocity is:

A

25 m/s

B

40 m/s

C

12.5 m/s

D

31.25 m/s

Question 225: Palette 225/345

Allen MCQ

An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the angle of projection with the horizontal is:

A

$\tan^{-1}\left(\frac{4}{5}\right)$

B

$\tan^{-1}\left(\frac{5}{4}\right)$

C

$\tan^{-1}\left(\frac{5}{8}\right)$

D

$\tan^{-1}\left(\frac{8}{5}\right)$

Question 226: Palette 226/345

Allen MCQ

A projectile is thrown into space so as to have the maximum possible horizontal range equal to 200m. Taking the point of projection as the origin, the coordinates of the point where the velocity of the projectile is minimum are:

A

(200, 100) m

B

(50, 200) m

C

(100, 50) m

D

(50, 100) m

Question 227: Palette 227/345

Allen MCQ

If the range of a gun which fires a shell with muzzle speed v, is R, then the angle of elevation of the gun is:

A

$\cos^{-1}\left(\frac{v^{2}}{Rg}\right)$

B

$\cos^{-1}\left(\frac{Rg}{v^{2}}\right)$

C

$\frac{1}{2}\sin^{-1}\left(\frac{v^{2}}{Rg}\right)$

D

$\frac{1}{2}\sin^{-1}\left(\frac{Rg}{v^{2}}\right)$

Question 228: Palette 228/345

Allen MCQ

Two balls A and B are thrown with speeds u and u/2 respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is $30^{\circ}$ with the horizontal, then the angle of projection of A is:

A

$\sin^{-1}\left(\frac{1}{8}\right)$

B

$\frac{1}{2}\sin^{-1}\left(\frac{\sqrt{3}}{8}\right)$

C

$\frac{1}{3}\sin^{-1}\left(\frac{1}{8}\right)$

D

$\frac{1}{4}\sin^{-1}\left(\frac{1}{8}\right)$

Question 229: Palette 229/345

Allen MCQ

Two balls are projected from the same point on the ground simultaneously. First ball is projected vertically upwards and the second ball at an angle of projection $60^{\circ}$ from the horizontal. Both the balls reach the ground simultaneously. The ratio of their velocities of projection are:

A

1:2

B

3:2

C

$\sqrt{3}$ :2

D

2:3

Question 230: Palette 230/345

Allen MCQ

A body is projected at an angle $\theta$ with horizontal, another body is projected with the same speed at an angle $\theta$ with the vertical then the ratio of the maximum height is:

A

$1:1$

B

$\tan^2\theta:1$

C

$1:\cot\theta$

D

none of these

Question 231: Palette 231/345

Allen MCQ

A ball is thrown from a point on earth surface with a speed v at an angle of projection θ from horizontal. From the same point and at the same instant a person starts running with a constant speed $\frac{v}{2}$ to catch the ball. The angle of projection of the ball from horizontal is:

A

60°

B

30°

C

90°

D

45°

Question 232: Palette 232/345

Allen MCQ

For a projectile the ratio of maximum height reached to the square of flight time is $(g=10\ m/s^{2})$ :-

A

5:4

B

5:2

C

5:1

D

10:1

Question 233: Palette 233/345

Allen MCQ

At what angle to the horizontal should a ball be thrown so that its range R is related to the time of flight T as $R = 5\sqrt{3}T^{2}$ ? Take $g = 10 ms^{-2}$ :

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$90^{\circ}$

Question 234: Palette 234/345

Allen MCQ

A ball whose kinetic energy is E, is thrown at an angle of $60^{\circ}$ to the horizontal. Its kinetic energy at the highest point of its flight will be:-

A

$\frac{E}{4}$

B

$\frac{E}{\sqrt{2}}$

C

$\frac{E}{2}$

D

zero

Question 235: Palette 235/345

Allen MCQ

A cricket ball is hit at an angle of $30^{\circ}$ with the vertical with kinetic energy K. The kinetic energy of the ball at the highest point of the path is :-

A

Zero

B

K/4

C

K/2

D

3K/4

Question 236: Palette 236/345

Allen MCQ

A ball is projected vertically upwards with a certain speed. Another ball of the same mass is projected at an angle $30^{\circ}$ to the vertical with the same initial speed. The ratio of their potential energies at highest points of their journey, will be

A

4:3

B

2:1

C

3:2

D

4:1

Question 237: Palette 237/345

Allen MCQ

A particle is projected with a velocity u making an angle $\theta$ with the horizontal. At any instant, its velocity v is at right angle to its initial velocity u; then v is:

A

u cos $\theta$

B

u tan $\theta$

C

u cot $\theta$

D

u sec $\theta$

Question 238: Palette 238/345

Allen MCQ

A force $\vec{\mathrm{F}} = (6\mathrm{t}^2\hat{\mathrm{i}} +4\mathrm{t}\hat{\mathrm{j}})\mathrm{N}$ acts on a particle of mass $1\mathrm{kg}$ . What will be velocity of the particle at $t = 3$ second if at $t = 0$ , the particle was at rest:

A

$(54\hat{\mathrm{i}} +12\hat{\mathrm{j}})\mathrm{m / s}$

B

$(54\hat{\mathrm{i}} +18\hat{\mathrm{j}})\mathrm{m / s}$

C

$(12\hat{\mathrm{i}} +6\hat{\mathrm{j}})\mathrm{m / s}$

D

none

Question 239: Palette 239/345

Allen MCQ

A stone is projected horizontally with a speed 10 m/s from a 80 m high building. The distance of the target on the ground from the foot of the building is: $(g = 10 \, \text{m/s}^2)$

A

80 m

B

40 m

C

20 m

D

10 m

Question 240: Palette 240/345

Allen MCQ

An aeroplane moving horizontally with a speed of 90 km/h drops a food packet while flying at a height of 490 m. The horizontal range of the packet is:

A

180 m

B

250 m

C

500 m

D

670 m

Question 241: Palette 241/345

Allen MCQ

A stuntman plans to run along a roof top and then horizontally off it to land on the roof of next building. The roof of the next building is 19.6 metres below the first one and 6.2 metres away from it. What should be his minimum roof top speed in m/s, so that he can successfully make the jump?

A

3.1

B

4.0

C

4.9

D

6.2

Question 242: Palette 242/345

Allen MCQ

Two stones are projected horizontally from the same height with speeds 100 m/s and 40 m/s. The ratio of their horizontal range is

A

1:1

B

5:2

C

2:5

D

3:4

Question 243: Palette 243/345

Allen MCQ

A body is thrown horizontally with a velocity 20 m/s from the top of a tower of height 20 m. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is :-

A

20 m

B

10 m

C

40 m

D

30 m

Question 244: Palette 244/345

Allen MCQ

A bomber is flying horizontally with a constant speed of 150 m/s at a height of 19.6 m. The pilot has to drop a bomb at the enemy target. At what horizontal distance from the target should he release the bomb?

A

0 m

B

300 m

C

600 m

D

1000 m

Question 245: Palette 245/345

Allen MCQ

A boy wants to jump from building A to building B. Height of building A is 25 m and that of building B is 5m. Distance between buildings is 8m. Assume that the boy jumps horizontally, then calculate minimum velocity with which he has to jump to land safely on building B.

A

$6\mathrm{m / s}$

B

$8\mathrm{m / s}$

C

$4\mathrm{m / s}$

D

$2\mathrm{m / s}$

Question 246: Palette 246/345

Allen MCQ

A boy wants to jump from building A to building B. Height of building A is 39.2 m and building B is 19.6m. Distance between buildings is 20 m. Assuming boy jumps horizontally, then calculate minimum velocity with which boy has to jump to land safely on building B :-

A

$10\mathrm{m / s}$

B

$20\mathrm{m / s}$

C

$9.8\mathrm{m / s}$

D

$19.6\mathrm{m / s}$

Question 247: Palette 247/345

Allen MCQ

Two buildings are separated by 30 m. By what speed a ball is projected horizontally from a window at height 150 m in one building so as to enter in the window at height 27.5 m in the other building.

A

2 m/s

B

6 m/s

C

4 m/s

D

8 m/s

Question 248: Palette 248/345

Allen MCQ

Two bodies of masses 100 kg and 50 kg are projected horizontally from same height with speeds 40 m/s and 20 m/s, simultaneously. The ratio of time taken by both the bodies to reach the ground is:-

A

1:1

B

1:2

C

2:1

D

1:4

Question 249: Palette 249/345

Allen MCQ

A ball is thrown horizontally from a height of 90 m with a speed of 4.5 m/s then find the time when it is at the height of 45 m from the ground:

A

$3\sqrt{2}$ sec

B

10 sec

C

9 sec

D

3 sec

Question 250: Palette 250/345

Allen MCQ

When a particle is thrown horizontally with speed u from top of tower, the displacement of the projectile at any time t is given by:

A

$\sqrt{u^{2}t^{2}+g^{2}t^{2}}$

B

$\sqrt{u^{2}t^{2}+\frac{1}{4}g^{2}t^{4}}$

C

$\sqrt{u^{2}+g^{2}t^{2}}$

D

$\sqrt{u^{2}-g^{2}t^{2}}$

Question 251: Palette 251/345

Allen MCQ

A plane is flying horizontally at $98\sqrt{3}$ m/s and releases an object which reaches the ground in 10 s. The angle made by it with horizontal while hitting the ground is:

A

$55^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$30^{\circ}$

Question 252: Palette 252/345

Allen MCQ

From the top of a tower 78.4 m high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of $45^{\circ}$ with the horizontal, then the initial velocity of the ball is:

A

9.8 m/s

B

4.9 m/s

C

19.6 m/s

D

2.8 m/s

Question 253: Palette 253/345

Allen MCQ

A particle is projected horizontally with a speed of $\frac{20}{\sqrt{3}}$ m/s, from some height at t = 0. At what time will its velocity make $30^{\circ}$ angle with the initial velocity

A

1 sec

B

2 sec

C

1.5 sec

D

$2/3$ sec

Question 254: Palette 254/345

Allen MCQ

In the above question what will be the displacement of the particle in x-direction when its velocity makes $30^{\circ}$ angle with the initial velocity

A

$\frac{20}{\sqrt{3}}$ m

B

$\frac{40}{3\sqrt{3}}$ m

C

$\frac{50}{\sqrt{3}}$ m

D

$\frac{10}{\sqrt{3}}$ m

Question 255: Palette 255/345

Allen MCQ

A ball is projected upwards from the top of a tower with a velocity of 50 m/s making an angle of $30^{\circ}$ with the horizontal. The height of the tower is 70m. After how much time from the instant of throwing, will the ball reach the ground?

A

2 s

B

5 s

C

7 s

D

9 s

Question 256: Palette 256/345

Allen MCQ

Which one of the following represents the displacement-time graph of two objects A and B moving with zero relative speed :-

A

B

C

D

Question 257: Palette 257/345

Allen MCQ

A monkey is climbing up a tree at a speed of 3 m/s. A dog runs towards the tree with a speed of 4 m/s. What is the relative speed of the dog as seen by the monkey?

A

> 7 m/s

B

Between 5 m/s and 7 m/s

C

5 m/s

D

< 5 m/s

Question 258: Palette 258/345

Allen MCQ

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is:-

A

East-north direction

B

West-north direction

C

South-east direction

D

None of these

Question 259: Palette 259/345

Allen MCQ

Two car A & B start from rest (from the same point) in same direction with acceleration 8 m/s² & 4 m/s² respectively then acceleration of car B in frame of A(Take direction of motion of car is positive) :-

A

4 m/s²

B

-4 m/s²

C

12 m/s²

D

None of these

Question 260: Palette 260/345

Allen MCQ

A motorcycle is moving with a velocity of 80 km/h and a car is moving with a velocity of 65 km/h in the opposite direction. What is the relative velocity of the motorcycle with respect to the car?

A

15 km/h

B

20 km/h

C

25 km/h

D

145 km/h

Question 261: Palette 261/345

Allen MCQ

Two cars A and B start moving from the same point with same speed v = 5 km/minute. Car A moves towards south and car B is moving towards west. What is the relative velocity of B with respect to A?

A

$5\sqrt{2}$ km/min towards South-East

B

$5\sqrt{2}$ km/min towards North-West

C

$5\sqrt{2}$ km/min towards South-West

D

$5\sqrt{2}$ km/min towards North-East

Question 262: Palette 262/345

Allen MCQ

A train is moving towards East with a speed 20 m/s. A person is running on the roof of the train with a speed 3 m/s in the direction of motion of train. Velocity of the person as seen by an observer on ground will be :

A

23 m/s towards East

B

17 m/s towards East

C

23 m/s towards West

D

17 m/s towards West

Question 263: Palette 263/345

Allen MCQ

A jet air plane travelling with a speed of 500 km/h ejects its products of combustion with a speed of 1600 km/h relative to the jet plane. The speed of the latter with respect to an observer on the ground is:-

A

1600 km/h

B

2100 km/h

C

1100 km/h

D

500 km/h

Question 264: Palette 264/345

Allen MCQ

A train moves in north direction with a speed of 54 km/h. A monkey is running on the roof of the train, against its motion with a velocity of 36 km/h. with respect to train. The velocity of monkey as observed by a man standing on the ground is:

A

5 m/s due north

B

25 m/s due south

C

10 m/s due south

D

10 m/s due north

Question 265: Palette 265/345

Allen MCQ

A lift is moving upwards with acceleration a. A man in the lift drops a ball within the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively:

A

g, g

B

g - a, g - a

C

g + a, g

D

a, g

Question 266: Palette 266/345

Allen MCQ

A stone is thrown upwards and it rises to a height of 200 m. The relative velocity of the stone with respect to the earth will be minimum at:-

A

Height of 100 m

B

Height of 150 m

C

Highest point

D

The ground

Question 267: Palette 267/345

Allen MCQ

A 100 m long train crosses a man travelling at 5 km/h, in opposite direction in 6 seconds, then the velocity of train is:-

A

40 km/h

B

55 km/h

C

20 km/h

D

45 km/h

Question 268: Palette 268/345

Allen MCQ

A 300 metres long train is moving due north with a speed of 20 m/s. A small bird is flying due south a little above the train with 5 m/s speed The time taken by the bird to cross the train is :-

A

6 s

B

7 s

C

9 s

D

12 s

Question 269: Palette 269/345

Allen MCQ

Two trains each 100 m long, are travelling in opposite directions with respective velocities 35 m/s and 15 m/s. The time of crossing is:-

A

2 s

B

4 s

C

$2\sqrt{3}s$

D

$4\sqrt{3}s$

Question 270: Palette 270/345

Allen MCQ

A train 200 m long crosses a bridge 300 m long. It enters the bridge with a speed of 30 ms $^{-1}$ and leaves it with a speed of 50 ms $^{-1}$ . What is the time taken to cross the bridge?

A

2.5s

B

7.5s

C

12.5s

D

15.0s

Question 271: Palette 271/345

Allen MCQ

Two cars get closer by 8 m in every second while travelling in the opposite directions. They get closer by 0.8 m in every second while travelling in the same direction. What are the speeds of the two cars?

A

$4 \, ms^{-1}$ and $4.4 \, ms^{-1}$

B

$4.4 \, ms^{-1}$ and $3.6 \, ms^{-1}$

C

$4 \, ms^{-1}$ and $3.6 \, ms^{-1}$

D

$4 \, ms^{-1}$ and $3 \, ms^{-1}$

Question 272: Palette 272/345

Allen MCQ

Velocity of a swimmer in still water is 5 m/s. If he takes 10 sec to swim upstream a distance of 30 m, then the speed of river is :-

A

3 m/s

B

5 m/s

C

10 m/s

D

2 m/s

Question 273: Palette 273/345

Allen MCQ

Two cars are moving in the same direction with the same speed of 60 km/h. They are separated by 10 km. What is the speed of a car moving in the opposite direction if it meets the two cars at an interval of 5 minute?

A

45 km/h

B

60 km/h

C

105 km/h

D

None

Question 274: Palette 274/345

Allen MCQ

Four persons P, Q, R and S of same mass travel with same speed u along a square of side 'd' such that each one always faces the other. After what time will they meet each other?

A

$\frac{\mathrm{d}}{\mathrm{u}}$

B

$\frac{2\mathrm{d}}{3\mathrm{u}}$

C

$\frac{2\mathrm{d}}{\mathrm{u}}$

D

$\mathrm{d}\sqrt{3}\mathrm{u}$

Question 275: Palette 275/345

Allen MCQ

Six persons of same mass travel with same speed u along a regular hexagon of side 'd' such that each one always faces the other. After how much time will they meet each other?

A

$\frac{\mathrm{d}}{\mathrm{u}}$

B

$\frac{2\mathrm{d}}{3\mathrm{u}}$

C

$\frac{2\mathrm{d}}{\mathrm{u}}$

D

$\mathrm{d}\sqrt{3}\mathrm{u}$

Question 276: Palette 276/345

Allen MCQ

A person walks up a stalled escalator in 45 sec. He is carried in 60s, when standing on the same escalator which is now moving. The time he would take to walk up the moving escalator will be :-

A

27 s

B

72 s

C

18 s

D

25.71 s

Question 277: Palette 277/345

Allen MCQ

A bus starts from rest moving with an acceleration of $2 \, m/s^{2}$ . A cyclist, 96 m behind the bus starts simultaneously towards the bus at 20 m/s. After what time will he be able to overtake the bus:-

A

8 s

B

10 s

C

12 s

D

1 s

Question 278: Palette 278/345

Allen MCQ

A boat takes 2 hours to go 10 km and come back in still water lake. The time taken for going 10 km upstream and coming back with water velocity of 5 km/h is:

A

140 min

B

150 min

C

160 min

D

170 min

Question 279: Palette 279/345

Allen MCQ

A river 2 km wide flows at the rate of 2km/h. A boatman who can row a boat at a speed of 6 km/h in still water, goes a distance of 2 km upstream and then comes back. The time taken by him to complete his journey is

A

60 min

B

45 min

C

80 min

D

90 min

Question 280: Palette 280/345

Allen MCQ

Two bodies are held separated by 9.8 m vertically one above the other. They are released simultaneously to fall freely under gravity. After 2 s the relative distance between them is :-

A

4.9 m

B

19.6 m

C

9.8 m

D

39.2m

Question 281: Palette 281/345

Allen MCQ

Two balls are thrown simultaneously, (A) vertically upwards with a speed of 20 m/s from the ground and (B) vertically downwards from a height of 80 m with the same speed and along the same line of motion. At which point will the balls collide? (take g = 10 m/s $^{2}$ )

A

15 m above from the ground

B

15 m below from the top of the tower

C

20 m above from the ground

D

20 m below from the top of the tower

Question 282: Palette 282/345

Allen MCQ

While sitting on a tree branch 20m above the ground, you drop a walnut. When the walnut has fallen 5m, you throws a second walnut straight down. What initial speed must you give the second walnut if they are both to reach the ground at the same time? $(g=10ms^{-2})$

A

$5 ms^{-1}$

B

$10 ms^{-1}$

C

$15 ms^{-1}$

D

None of these

Question 283: Palette 283/345

Allen MCQ

A body A is thrown up vertically from the ground with velocity $v_{0}$ and another body B is simultaneously dropped from a height H. They meet at a height $\frac{H}{2}$ if $v_{0}$ is equal to

A

$\sqrt{2gH}$

B

$\sqrt{gH}$

C

$\frac{1}{2}\sqrt{gH}$

D

$\sqrt{\frac{2g}{H}}$

Question 284: Palette 284/345

Allen MCQ

An elevator is accelerating upward at a rate of $6 \, ft/sec^{2}$ when a bolt from its ceiling falls to the floor of the lift (Distance = 19 feet). The time (in seconds) taken by the falling bolt to hit the floor is (take g = 32 ft/ sec $^{2}$ )

A

$\sqrt{2}$

B

1

C

$2\sqrt{2}$

D

$\frac{1}{2\sqrt{2}}$

Question 285: Palette 285/345

Allen MCQ

A boat is sent across a river with a velocity of 8km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is

A

10 km/hr

B

8 km/hr

C

6 km/hr

D

4 km/hr

Question 286: Palette 286/345

Allen MCQ

A bird is flying towards south with a velocity 40km/h and a train is moving with a velocity 40 km/h towards east. What is the velocity of the bird w.r.t. an observer in the train?

A

$40 \sqrt{2}$ km/h. N-E

B

$40 \sqrt{2}$ km/h. S-E

C

$40 \sqrt{2}$ km/h. S-W

D

$40 \sqrt{2}$ km/h. N-W

Question 287: Palette 287/345

Allen MCQ

A bird is flying with a speed of 40 km/h in the north direction. A train is moving with a speed of 30 km/h in the west direction. A passenger sitting in the train will see the bird moving with velocity:

A

50 km/hr, 53° North of east

B

50 km/hr, 37° North of east

C

50 km/hr, 53° East of north

D

50 km/hr in North East direction

Question 288: Palette 288/345

Allen MCQ

A boat is sailing with a velocity $(3\hat{i}+4\hat{j})$ with respect to ground and water in river is flowing with a velocity $(-6\hat{i}-8\hat{j})$ . Relative velocity of the boat with respect to water is:

A

$8\hat{j}$

B

$9\hat{i}+12\hat{j}$

C

$6\hat{i}+8\hat{j}$

D

$-6\hat{i}-8\hat{j}$

Question 289: Palette 289/345

Allen MCQ

Let $\vec{r}_1(t) = 3\hat{t}i + 4t^2\hat{j}$ and $\vec{r}_2(t) = 4t^2\hat{i} + 3t\hat{j}$ represent the positions of particles 1 and 2, respectively as functions of time t; $\vec{r}_1(t)$ and $\vec{r}_2(t)$ are in metres and t is in seconds. The relative speed of the two particles at the instant $t = 2$ sec, will be

A

$1\mathrm{m / s}$

B

$13\sqrt{2}\mathrm{m / s}$

C

$5\sqrt{2}\mathrm{m / s}$

D

$7\sqrt{2}\mathrm{m / s}$

Question 290: Palette 290/345

Allen MCQ

Rain is falling vertically with a speed of 3 m/s. If a man is running with the same speed then the velocity of rain w.r.t. man is :-

A

3 m/s

B

6 m/s

C

4.2 m/s

D

0 m/s

Question 291: Palette 291/345

Allen MCQ

A man is walking on a road with a velocity of 5km/h. When suddenly it starts raining, velocity of rain is 10km/h in vertically downward direction, relative velocity of the rain with respect to man is:

A

$\sqrt{13}$ km/hr

B

$\sqrt{7}$ km/hr

C

$\sqrt{109}$ km/hr

D

$5\sqrt{5}$ km/hr

Question 292: Palette 292/345

Allen MCQ

If the rain is falling vertically downwards with velocity 20 m/s and if a bike is going with velocity 30 m/s. Calculate at what angle from the vertical a man on the bike must incline his umbrella so that he can save himself from rain:

A

$\tan^{-1}\left(\frac{2}{3}\right)$

B

$\tan^{-1}\left(\frac{3}{2}\right)$

C

$\tan^{-1}(1)$

D

$\tan^{-1}\left(\frac{6}{5}\right)$

Question 293: Palette 293/345

Allen MCQ

If rain is falling at some angle from vertical and has horizontal velocity 2 m/s in east direction. With what velocity a man must move on the horizontal surface so that rain will appear vertical to him :-

A

4 m/s in east direction

B

2 m/s in east direction

C

2 m/s in west direction

D

2 m/s in a circular path

Question 294: Palette 294/345

Allen MCQ

A boy is running on a levelled road with velocity (u) with a long hollow tube in his hand. Water is falling vertically downwards with velocity (v). At what angle to the vertical, should he incline the tube so that the water drops enters without touching its side:

A

$\tan^{-1}\left(\frac{v}{u}\right)$

B

$\sin^{-1}\left(\frac{v}{u}\right)$

C

$\tan^{-1}\left(\frac{u}{v}\right)$

D

$\cos^{-1}\left(\frac{v}{u}\right)$

Question 295: Palette 295/345

Allen MCQ

A river is flowing at the rate of 8 km/h. A swimmer swims across the river with a velocity of 10 km/h w.r.t. water. The resultant velocity of the man will be in (km/h):-

A

$\sqrt{117}$

B

$\sqrt{340}$

C

$\sqrt{164}$

D

$3\sqrt{40}$

Question 296: Palette 296/345

Allen MCQ

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the north :-

A

$30^{\circ}$ with downstream

B

$60^{\circ}$ with downstream

C

$120^{\circ}$ with downstream

D

South

Question 297: Palette 297/345

Allen MCQ

A river 4.0 miles wide is flowing at the rate of 2 miles/hr. The minimum time taken by a boat to cross the river with a speed v = 2 miles/hr (in still water) is approximately

A

1 hr and 0 minute

B

2 hr

C

1 hr and 12 minutes

D

2 hr and 25 minutes

Question 298: Palette 298/345

Allen MCQ

A river flows from east to west with a speed of 5m/min. A man on south bank of river, capable of swimming at the rate of 10 m/min in still water, wants to swim across the river in shortest time; he should swim :

A

due north

B

due north-east

C

due north-east with double the speed of river

D

none of the above

Question 299: Palette 299/345

Allen MCQ

A boat-man can row a boat to make it move with a speed of 10 km/h in still water. River flows steadily at the rate of 6 km/h. and the width of the river is 4 km. If the boat man cross the river along the minimum distance of approach then time elapsed in rowing the boat will be:

A

$\frac{2\sqrt{3}}{5}$ h

B

$\frac{2}{5\sqrt{3}}$ h

C

$\frac{3\sqrt{2}}{5}$ h

D

$\frac{1}{2}$ h

Question 300: Palette 300/345

Allen MCQ

A man wishes to swim across a river 0.5 km wide. If he can swim at the rate of $\sqrt{2}$ km/h in still water and the river flows at the rate of 1 km/h. The angle made by the direction (w.r.t. the flow of the river) along which he should swim so as to reach a point exactly opposite his starting point, should be :

A

$60^{\circ}$

B

$120^{\circ}$

C

$135^{\circ}$

D

$90^{\circ}$

Question 301: Palette 301/345

Allen MCQ

Two particles are separated by a horizontal distance x as shown in figure. They are projected as shown in figure with different initial speeds. The time after which the horizontal distance between them becomes zero is :

A

$\frac{\mathbf{x}}{\mathbf{u}}$

B

$\frac{\mathrm{u}}{2\mathrm{x}}$

C

$\frac{\mathrm{x}}{2\mathrm{u}}$

D

none of these

Question 302: Palette 302/345

Allen MCQ

A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m/s $^{2}$ ) is: (given g = 9.8 m/s $^{2}$ )

A

3.5

B

5.9

C

16.3

D

110.8

Question 303: Palette 303/345

Allen MCQ

A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0 (6m, 7m) at time t = 2 s and (13m, 14m) at time t = 5s. Average velocity vector ( $\vec{V}_{av}$ ) from t = 0 to t = 5 s is

A

$\frac{1}{5}\left(13\hat{i} + 14\hat{j}\right)$

B

$\frac{7}{3}\left(\hat{i} + \hat{j}\right)$

C

$2\left(\hat{i} + \hat{j}\right)$

D

$\frac{11}{5}\left(\hat{i} + \hat{j}\right)$

Question 304: Palette 304/345

Allen MCQ

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$ where $\beta$ and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by:

A

$-2n\beta^{2}x^{-4n-1}$

B

$-2\beta^{2}x^{-2n+1}$

C

$-2n\beta^{2}e^{-4n+1}$

D

$-2n\beta^{2}x^{-2n-1}$

Question 305: Palette 305/345

Allen MCQ

A ship A is moving Westwards with a speed of 10 km/h and a ship B 100 km South of A, is moving Northwards with a speed of 10 km/h. The time after which the distance between them becomes shortest, is :-

A

5 h

B

$5\sqrt{2}$ h

C

$10\sqrt{2}$ h

D

0 h

Question 306: Palette 306/345

Allen MCQ

Two particles A and B, move with constant velocities $\vec{\mathbf{v}}_1$ and $\vec{\mathbf{v}}_2$ . At the initial moment their position vectors are $\vec{\mathbf{r}}_1$ and $\vec{\mathbf{r}}_2$ respectively. The condition for particle A and B for their collision is:-

A

$\vec{\mathbf{r}}_1 - \vec{\mathbf{r}}_2 = \vec{\mathbf{v}}_1 - \vec{\mathbf{v}}_2$

B

$\frac{\vec{\mathbf{r}}_1 - \vec{\mathbf{r}}_2}{|\vec{\mathbf{r}}_1 - \vec{\mathbf{r}}_2|} = \frac{\vec{\mathbf{v}}_2 - \vec{\mathbf{v}}_1}{|\vec{\mathbf{v}}_2 - \vec{\mathbf{v}}_1|}$

C

$\vec{\mathbf{r}}_1 \cdot \vec{\mathbf{v}}_1 = \vec{\mathbf{r}}_2 \cdot \vec{\mathbf{v}}_2$

D

$\vec{\mathbf{r}}_1 \times \vec{\mathbf{v}}_1 = \vec{\mathbf{r}}_2 \times \vec{\mathbf{v}}_2$

Question 307: Palette 307/345

Allen MCQ

If the velocity of a particle is $v = At + Bt^{2}$ , where A and B are constants, then the distance travelled by it between 1s and 2s is:

A

$\frac{3}{2}A + 4B$

B

$3A + 7B$

C

$\frac{3}{2}A + \frac{7}{3}B$

D

$\frac{A}{2} + \frac{B}{3}$

Question 308: Palette 308/345

Allen MCQ

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_{p}(t) = at + bt^{2}$ and $x_{Q}(t) = ft - t^{2}$ . At what time do the cars have the same velocity?

A

$\frac{a+f}{2(1+b)}$

B

$\frac{f-a}{2(1+b)}$

C

$\frac{a-f}{1+b}$

D

$\frac{a+f}{2(b-1)}$

Question 309: Palette 309/345

Allen MCQ

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_{1}$ . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_{2}$ . The time taken by her to walk up on the moving escalator will be

A

$\frac{t_{1}t_{2}}{t_{2}-t_{1}}$

B

$\frac{t_{1}t_{2}}{t_{2}+t_{1}}$

C

$t_{1}-t_{2}$

D

$\frac{t_{1}+t_{2}}{2}$

Question 310: Palette 310/345

Allen MCQ

The x and y coordinates of the particle at any time are $x = 5t - 2t^{2}$ and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is:

A

$5 \, m/s^{2}$

B

$-4 \, m/s^{2}$

C

$-8 \, m/s^{2}$

D

0

Question 311: Palette 311/345

Allen MCQ

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:

A

30° west

B

0°

C

60° west

D

45° west

Question 312: Palette 312/345

Allen MCQ

When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal, it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object the shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}:x_{2}$ will be

A

$1:\sqrt{2}$

B

$\sqrt{2}:1$

C

$1:\sqrt{3}$

D

$1:2\sqrt{3}$

Question 313: Palette 313/345

Allen MCQ

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_{1}$ if the elevator is at rest and in time $t_{2}$ if the elevator is moving uniformly. Then:

A

$t_{1} < t_{2}$ or $t_{1} > t_{2}$ depending upon whether the lift is going up or down

B

$t_{1} < t_{2}$

C

$t_{1} > t_{2}$

D

$t_{1} = t_{2}$

Question 314: Palette 314/345

Allen MCQ

Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200m with the same velocity of 25 m/s. When and where will the two bullets collide. (g = 10 m/s $^{2}$ )

A

after 2s at a height 180 m

B

after 2s at a height of 20 m

C

after 4s at a height of 120 m

D

they will not collide

Question 315: Palette 315/345

Allen MCQ

A person travelling in a straight line moves with a constant velocity $v_{1}$ for certain distance 'x' and with a constant velocity $v_{2}$ for next equal distance. The average velocity v is given by the relation

A

$\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

B

$\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

C

$\frac{v}{2} = \frac{v_{1} + v_{2}}{2}$

D

$v = \sqrt{v_{1}v_{2}}$

Question 316: Palette 316/345

Allen MCQ

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: $(g = 10 \, \text{m/s}^2)$

A

300 m

B

360 m

C

340 m

D

320 m

Question 317: Palette 317/345

Allen MCQ

A person sitting in the ground floor of a building notices through the window, of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window? $(g = 10 \, \text{m/s}^2)$

A

15.5 m/s

B

14.5 m/s

C

4.5 m/s

D

20 m/s

Question 318: Palette 318/345

Allen MCQ

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let $S_{n}$ be the distance travelled by the block in the interval t = n - 1 to t = n. Then, the ratio $\frac{S_{n}}{S_{n+1}}$ is:

A

$\frac{2n-1}{2n}$

B

$\frac{2n-1}{2n+1}$

C

$\frac{2n+1}{2n-1}$

D

$\frac{2n}{2n-1}$

Question 319: Palette 319/345

Allen MCQ

A car starts from rest and accelerates at $5 \, m/s^{2}$ . At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6 \, s$ ? (Take $g = 10 \, m/s^{2}$ )

A

$20 \, m/s, 5 \, m/s^{2}$

B

$20 \, m/s, 0$

C

$20\sqrt{2} \, m/s, 0$

D

$20\sqrt{2} \, m/s, 10 \, m/s^{2}$

Question 320: Palette 320/345

Allen MCQ

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle 'θ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ, is then given by:

A

$\theta = \cos^{-1}\left(\frac{gT^{2}}{\pi^{2}R}\right)^{\frac{1}{2}}$

B

$\theta = \cos^{-1}\left(\frac{\pi^{2}R}{gT^{2}}\right)^{\frac{1}{2}}$

C

$\theta = \sin^{-1}\left(\frac{\pi^{2}R}{gT^{2}}\right)^{\frac{1}{2}}$

D

$\theta = \sin^{-1}\left(\frac{2gT^{2}}{\pi^{2}R}\right)^{\frac{1}{2}}$

Question 321: Palette 321/345

Allen MCQ

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the x-axis as shown in the figure. The ratio of their respective velocity is :

A

$1:1$

B

$1:2$

C

$1:\sqrt{3}$ $

D

\sqrt{3}:1$

Question 322: Palette 322/345

Allen MCQ

The ratio of the distances travelled by a freely falling body in the $1^{st}$ , $2^{nd}$ , $3^{rd}$ and $4^{th}$ second:

A

1:4:9:16

B

1:3:5:7

C

1:1:1:1

D

1:2:3:4

Question 323: Palette 323/345

Allen MCQ

A ball is projected with a velocity, $10 \, ms^{-1}$ , at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be:

A

$5\sqrt{3}ms^{-1}$

B

$5 \, ms^{-1}$

C

$10 \, ms^{-1}$

D

Zero

Question 324: Palette 324/345

Allen MCQ

A cricket ball is thrown by a player at a speed of 20 m/s in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is: $(g = 10 \, \text{m/s}^{2})$

A

5 m

B

10 m

C

20 m

D

25 m

Question 325: Palette 325/345

Allen MCQ

The position-time $(x - t)$ graph for positive acceleration is :

A

B

C

D

Question 326: Palette 326/345

Allen MCQ

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is:

A

$\frac{2v}{3}$

B

$\frac{4v}{3}$

C

$\frac{3v}{4}$

D

$\frac{v}{3}$

Question 327: Palette 327/345

Allen MCQ

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \, ms^{-1}$ . The ball strikes the water surface after 4s. The height of bridge above water surface is (Take g = $10 \, m \, s^{-2}$ )

A

60 m

B

64 m

C

68 m

D

56 m

Question 328: Palette 328/345

Allen MCQ

A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$ . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

A

24 cm

B

28 cm

C

30 cm

D

27 cm

Question 329: Palette 329/345

Allen MCQ

The position of a particle is given by $\vec{r}(t) = 4t\hat{i} + 2t^2\hat{j} + 5\hat{k}$ where t is in seconds and r in metre. Find the magnitude and direction of velocity v(t), at t = 1s, with respect to x-axis

A

$4\sqrt{2} \text{ ms}^{-1}$ , $45^\circ$

B

$4\sqrt{2} \text{ ms}^{-1}$ , $60^\circ$

C

$3\sqrt{2} \text{ ms}^{-1}$ , $30^\circ$

D

$3\sqrt{2} \text{ ms}^{-1}$ , $45^\circ$

Question 330: Palette 330/345

Allen MCQ

A ball is projected from point A with velocity $20 \, m s^{-1}$ at an angle $60^{\circ}$ to the horizontal direction. At the highest point B of the path (as shown in figure), the velocity $v \, m s^{-1}$ of the ball will be:

A

20

B

$10\sqrt{3}$

C

Zero

D

10

Question 331: Palette 331/345

Allen MCQ

The velocity (v) - time (t) plot of the motion of a body is shown below: The acceleration $(a)$ - time $(t)$ graph that best suits this motion is:

A

B

C

D

Question 332: Palette 332/345

Allen MCQ

A particle is moving along x-axis with its position (x) varying with time (t) as $x = \alpha t^{4} + \beta t^{2} + \gamma t + \delta$ . The ratio of its initial velocity to its initial acceleration, respectively is:

A

$2\alpha:\delta$

B

$\gamma:2\delta$

C

$4\alpha:\beta$

D

$\gamma:2\beta$

Question 333: Palette 333/345

Allen MCQ

For ground to ground projectile motion with initial velocity u at angle $\theta$ from horizontal. Match Column-I with Column-II

Column-I	Column-II
(P) Change in speed from initial to final point (Q) Magnitude of change in velocity from initial to final point (R) Change in speed from initial to top (S) Magnitude of change in velocity from initial to top	(I) $u-u\cos\theta$ (II) $u\sin\theta$ (III) $2u\sin\theta$ (IV) zero

A

P-I, Q-II, R-III, S-IV

B

P-IV, Q-II, R-I, S-III

C

P-IV, Q-III, R-I, S-II

D

P-IV, Q-III, R-II, S-I

Question 334: Palette 334/345

Allen MCQ

For initial velocity $(\vec{v}_{i})=3\hat{i}-4\hat{j}$ and final velocity $(\vec{v}_{f})=3\hat{i}+4\hat{j}$ :Match Column-I with Column-II

Column-I	Column-II
(P) $|\Delta \vec{v}|$ (Q) $\Delta |\vec{v}|$ (R) $\vec{v}_f-\vec{v}_i$ (S) $\vec{v}_f+\vec{v}_i$	(I) $8\hat{j}$ (II) $6\hat{i}$ (III) $0$ (IV) $8$

A

P-III, Q-IV, R-II, S-I

B

P-III, Q-IV, R-I, S-II

C

P-IV, Q-III, R-II, S-I

D

P-IV, Q-III, R-I, S-II

Question 335: Palette 335/345

Allen MCQ

A particle is projected vertically upward from ground with initial velocity u such that it clears the top of a pole of height h after time $t_{1}$ in its path. It takes further time $t_{2}$ to reach the ground. Match Column-I with Column-II

Column-I	Column-II
(P) $u$ (Q) $h$ (R) Time of flight (S) Maximum height	(I) $\dfrac{(t_1+t_2)^2}{8}g$ (II) $(t_1+t_2)$ (III) $\dfrac{1}{2}g(t_1+t_2)$ (IV) $\dfrac{1}{2}gt_1t_2$

A

P-II, Q-I, R-III, S-IV

B

P-I, Q-II, R-III, S-IV

C

P-III,Q-IV, R-II, S-I

D

P-IV, Q-II, R-II, S-I

Question 336: Palette 336/345

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Horizontal component of velocity is constant in projectile motion under gravity.
Reason (R) : Two projectiles having same horizontal range must have the same time of flight.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 337: Palette 337/345

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A particle with constant acceleration always moves along a straight line.
Reason (R): A particle with constant acceleration will not change direction of motion.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

Both (A) and (R) are false.

Question 338: Palette 338/345

Allen MCQ

An object may have-
(A) varying speed without having varying velocity
(B) varying velocity without having varying speed
(C) non-zero acceleration without having varying velocity
(D) non-zero acceleration without having varying speed

A

Only B is correct

B

Only D is correct

C

Both B and D are correct

D

All are correct

Question 339: Palette 339/345

Allen MCQ

The velocity of a particle is zero at t = 0, then -

(A) the acceleration at t = 0 must be zero

(B) the acceleration at t = 0 may be zero

(C) if the acceleration is zero from t = 0 to t = 10 s, speed is also zero in this interval

(D) if the speed is zero from t = 0 to t = 10 sec, the acceleration is also zero in the interval

A

(A), (C) and (D) are correct

B

(B), (C) and (D) are correct

C

(A) and (D) are correct

D

(B) and (C) are correct

Question 340: Palette 340/345

Allen MCQ

Instantaneous velocity of a particle - (A) depends on instantaneous position (B) depends on instantaneous speed (C) independent of instantaneous position (D) independent of instantaneous speed

A

Both (A) & (B) are correct

B

Both (C) & (D) are correct

C

Both (A) & (D) are correct

D

Both (B) & (C) are correct

Question 341: Palette 341/345

Allen MCQ

If the velocity of a body is constant - (A) $|Velocity| = speed$ (B) $|Average velocity| = speed$ (C) $Velocity = average velocity$ (D) $Speed = average speed$

A

Only (A) is correct

B

(A) and (B) are correct

C

(C) and (D) are correct

D

All are correct

Question 342: Palette 342/345

Allen MCQ

A moving particle is acted upon by three forces at different times to bring it to rest. Its velocity versus time graph is given below The average speed for the first 6 s is

A

zero

B

$\frac{5}{3} \mathrm{~ms}^{-1}$

C

$\frac{10}{3} \mathrm{~ms}^{-1}$

D

$\frac{20}{3} \mathrm{~ms}^{-1}$

Question 343: Palette 343/345

Allen MCQ

A moving particle is acted upon by three forces at different times to bring it to rest. Its velocity versus time graph is given below The average velocity for the first 12s is

A

zero

B

5 m/s

C

$\frac{10}{3}$ m/s

D

10 m/s

Question 344: Palette 344/345

Allen MCQ

A moving particle is acted upon by three forces at different times to bring it to rest. Its velocity versus time graph is given below The average acceleration from t = 5s to t = 15s is

A

zero

B

-0.5 m/s²

C

+0.5 m/s²

D

1 m/s²

Question 345: Palette 345/345

Allen MCQ

Match the entries in column I with points on graph.

Column-I	Column-II
(A) $x \rightarrow$ negative, $v \rightarrow$ positive, $a \rightarrow$ positive (B) $x \rightarrow$ positive, $v \rightarrow$ negative, $a \rightarrow$ negative (C) $x \rightarrow$ negative, $v \rightarrow$ negative, $a \rightarrow$ positive (D) $x \rightarrow$ positive, $v \rightarrow$ positive, $a \rightarrow$ negative	(P) P (Q) Q (R) R (S) S

A

A → S, B → Q, C → R, D → P

B

A → P, B → R, C → Q, D → S

C

A → S, B → R, C → Q, D → P

D

A → S, B → Q, C → R, D → S