Question 1: Palette 1/135

Errorless CBSE PMT 2003 MCQ

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B

A

18m

B

6m

C

$\frac{2}{3}m$

D

$\frac{2}{9}m$

Question 2: Palette 2/135

Errorless CPMT 2003 MCQ

Two balls are dropped from heights h and 2h respectively from the earth surface. The ratio of time of these balls to reach the earth is

A

$1 : \sqrt{2}$

B

$\sqrt{2} : 1$

C

2 : 1

D

1 : 4

Question 3: Palette 3/135

Errorless MP PET 2002 MCQ

The ratio of the numerical values of the average velocity and average speed of a body is always

A

Unity

B

Unity or less

C

Unity or more

D

Less than unity

Question 4: Palette 4/135

Errorless MP PMT 2002 MCQ

A body falling from a high Minaret travels 40 meters in the last 2 seconds of its fall to ground. Height of Minaret in meters is (take $g = 10m / s^2$ )

A

60

B

45

C

80

D

50

Question 5: Palette 5/135

Errorless Kerala PMT 2002 MCQ

A cricket ball is thrown up with a speed of $19.6 \, ms^{-1}$ . The maximum height it can reach is

A

9.8 m

B

19.6 m

C

29.4 m

D

39.2 m

Question 6: Palette 6/135

Errorless AIIMS 2002 MCQ

Three different objects of masses $m_1, m_2$ and $m_3$ are allowed to fall from rest and from the same point 'O' 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 7: Palette 7/135

Errorless Kerala (Engg.) 2001 MCQ

A particle moves along a semicircle of radius 10m in 5 seconds. The velocity of the particle is

A

$2\pi ms^{-1}$

B

$4\pi ms^{-1}$

C

$2 ms^{-1}$

D

$4 ms^{-1}$

Question 8: Palette 8/135

Errorless CBSE PMT 2001 MCQ

A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of length 850 meters is

A

56 sec

B

68 sec

C

80 sec

D

92 sec

Question 9: Palette 9/135

Errorless MP PMT 2001 MCQ

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

A

0 meter

B

2 meter

C

3 meter

D

- 2 meter

Question 10: Palette 10/135

Errorless DCE 2001; AIIMS 2002 MCQ

A particle starts from rest, accelerates at $2 \, m/s^{2}$ for 10s and then goes for constant speed for 30s and then decelerates at $4 \, m/s^{2}$ till it stops. What is the distance travelled by it

A

750 m

B

800 m

C

700 m

D

850 m

Question 11: Palette 11/135

Errorless UPSEAT 2001 MCQ

A particle when thrown, moves such that it passes from same height at 2 and 10s, the height is

A

g

B

2g

C

5g

D

8g

Question 12: Palette 12/135

Errorless DCE 2000 MCQ

A body moves 6 m north. 8 m east and 10 m vertically upwards, what is its resultant displacement from initial position

A

$10\sqrt{2}m$

B

10m

C

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

D

$10\times2m$

Question 13: Palette 13/135

Errorless BHU 2000 MCQ

A body is moving according to the equation $x = at + bt^{2} - ct^{3}$ where x = displacement and a, b and c are constants. The acceleration of the body is

A

$a + 2bt$

B

$2b + 6ct$

C

$2b - 6ct$

D

$3b - 6ct^{2}$

Question 14: Palette 14/135

Errorless MP PMT 2000; RPET 2001 MCQ

A body of 5 kg is moving with a velocity of 20 m/s. If a force of 100 N is applied on it for 10s in the same direction as its velocity, what will now be the velocity of the body

A

200 m/s

B

220 m/s

C

240 m/s

D

260 m/s

Question 15: Palette 15/135

Errorless CBSE PMT 2000; AFMC 2001 MCQ

A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statements about the motion of the particle is false

A

Displacement of the particle is zero

B

Average speed of the particle is 3 m/s

C

Displacement of the particle is 30 m

D

Both

Question 16: Palette 16/135

Errorless EAMCET (Engg.) 2000 MCQ

A constant force acts on a body of mass 0.9 kg at rest for 10s. If the body moves a distance of 250 m, the magnitude of the force is

A

3N

B

3.5N

C

4.0N

D

4.5N

Question 17: Palette 17/135

Errorless AIIMS 2000; CBSE PMT 2002 MCQ

From the top of a tower, a particle is thrown vertically down wards with a velocity of 10 m/s. The ratio of the distances covered by it in the $3^{rd}$ and $2^{nd}$ seconds of the motion is (Take $g = 10 \, m/s^{2}$ )

A

5:7

B

7:5

C

3:6

D

6:3

Question 18: Palette 18/135

Errorless EAMCET (Engg.) 2000 MCQ

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

A

1:1

B

11:1

C

1:2

D

1:11

Question 19: Palette 19/135

Errorless RPET 2000; KCET (Engg./Med.) 2001; DPMT 2001 MCQ

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

A

Equal to the time of fall

B

Less than the time of fall

C

Greater than the time of fall

D

Twice the time of fall

Question 20: Palette 20/135

Errorless RPET 1999 MCQ

Two cars A and B are at rest at same point initially. If A starts with uniform velocity of 40 m/sec and B starts in the same direction with constant acceleration of $4 \, m/s^{2}$ , then B will catch A after how much time

A

10 sec

B

20 sec

C

30 sec

D

35 sec

Question 21: Palette 21/135

Errorless RPMT 1999 MCQ

Time taken by an object to reach the height of $h_{1}$ and $h_{2}$ is respectively $t_{1}$ and $t_{2}$ then the ratio of $t_{1}$ to $t_{2}$ is

A

$h_{1}:h_{2}$

B

$\sqrt{h_{1}}:\sqrt{h_{2}}$

C

$h_{1}:2h_{2}$

D

$2h_{1}:h_{2}$

Question 22: Palette 22/135

Errorless AFMC 1999 MCQ

A stone is thrown with an initial speed of 4.9 m/s from a bridge in vertically upward direction. It falls down in water after 2 sec. The height of the bridge is

A

4.9 m

B

9.8 m

C

19.8 m

D

24.7 m

Question 23: Palette 23/135

Errorless SCRA 1998; DCE 2000 MCQ

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement (s) -velocity (v) graph of this object is

A

B

C

D

Question 24: Palette 24/135

Errorless SCRA 1998 MCQ

If a train travelling at 72 kmph to be brought to rest in distance of 200 metres, then its retardation should be

A

$20 ms^{-2}$

B

$10 ms^{-2}$

C

$2 ms^{-2}$

D

$1 ms^{-2}$

Question 25: Palette 25/135

Errorless CBSE PMT 1998, 99; AFMC 2000; JIPMER 2001, 02 MCQ

A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance

A

8 m

B

2 m

C

4 m

D

6 m

Question 26: Palette 26/135

Errorless MNR 1998 MCQ

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of

A

$3s$

B

$5s$

C

$7s$

D

$9s$

Question 27: Palette 27/135

Errorless AFMC 1997 MCQ

If a body starts from rest and travels 120 cm in the 6th second, then what is the acceleration

A

$0.20 \, m/s^{2}$

B

$0.027 \, m/s^{2}$

C

$0.218 \, m/s^{2}$

D

$0.03 \, m/s^{2}$

Question 28: Palette 28/135

Errorless BHU 1997; CPMT 1997 MCQ

A ball is dropped on the floor from a height of 10 m. It rebounds to a height 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is

A

$2100 \, m / sec^{2}$ downwards

B

$2100 \, m / sec^{2}$ upwards

C

$1400 \, m / sec^{2}$

D

$700 \, m / sec^{2}$

Question 29: Palette 29/135

Errorless RPET 1996 MCQ

A car moves for half of its time at 80 km/h and for rest half of time at 40 km/h. Total distance covered is 60 km. What is the average speed of the car

A

60 km/h

B

80 km/h

C

120 km/h

D

180 km/h

Question 30: Palette 30/135

Errorless CBSE PMT 1996; KCET 2002 MCQ

A body dropped from a height h with an initial speed zero, strikes the ground with a velocity 3 km/h. Another body of same mass is dropped from the same height h with an initial speed $-u' = 4 \, km/h$ . Find the final velocity of second body with which it strikes the ground

A

3 km / h

B

4 km / h

C

5 km / h

D

12 km / h

Question 31: Palette 31/135

Errorless EAMCET (Engg.)1995 MCQ

The displacement is given by $x = 2t^{2} + t + 5$ , the acceleration at t = 2s is

A

$4m/s^{2}$

B

$8m/s^{2}$

C

$10m/s^{2}$

D

$15m/s^{2}$

Question 32: Palette 32/135

Errorless MNR 1995; UPSEAT 2000 MCQ

The velocity of a body depends on time according to the equation $v = 20 + 0.1t^{2}$ . The body is undergoing

A

Uniform acceleration

B

Uniform retardation

C

Non-uniform acceleration

D

Zero acceleration

Question 33: Palette 33/135

Errorless MP PET 1995 MCQ

A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is

A

1 m / sec

B

10 m / sec

C

5 m / sec

D

2 m / sec

Question 34: Palette 34/135

Errorless EAMCET (Engg.) 1995 MCQ

A body is projected up with a speed ‘u’ and the time taken by it is T to reach the maximum height H. Pick out the correct statement

A

It reaches H/2 in T/2 sec

B

It acquires velocity u/2 in T/2 sec

C

Its velocity is u/2 at H/2

D

Same velocity at 2T

Question 35: Palette 35/135

Errorless CBSE PMT 1994; JIPMER 2001, 02 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 velocity when the acceleration is zero is

A

$3 ms^{-1}$

B

$-12 ms^{-1}$

C

$42 ms^{-1}$

D

$-9 ms^{-1}$

Question 36: Palette 36/135

Errorless ISM Dhanbad 1994 MCQ

P, Q and R are three balloons ascending with velocities U, 4U and 8U respectively. If stones of the same mass be dropped from each, when they are at the same height, then

A

They reach the ground at the same time

B

Stone from P reaches the ground first

C

Stone from R reaches the ground first

D

Stone from Q reaches the ground first

Question 37: Palette 37/135

Errorless NCERT 1990 MCQ

An athlete completes one round of a circular track of radius R in 40 seconds. What will be his displacement at the end of 2 minutes 20 seconds

A

Zero

B

2R

C

$2\pi R$

D

$7\pi R$

Question 38: Palette 38/135

Errorless NCERT 1990 MCQ

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is

A

Increasing with time

B

Decreasing with time

C

Constant but not zero

D

Zero

Question 39: Palette 39/135

Errorless CBSE PMT 1989 MCQ

A car travels a distance of 2000 m. If the first half distance is covered at 40 km/hour and the second half with speed v and the average speed is 48 km/hour, then the value of v is

A

56 km/hour

B

60 km/hour

C

50 km/hour

D

48 km/hour

Question 40: Palette 40/135

Errorless MNR 1987; MP PET 1996 MCQ

A particle moves along x-axis in such a way that its coordinate x varies with time t according to the equation $x = (2 - 5t + 6t^{2})m$ . The initial velocity of the particle is

A

-5 m/s

B

6 m/s

C

-3 m/s

D

3 m/s

Question 41: Palette 41/135

Errorless CPMT 1986 MCQ

The graph between the displacement x and time t for a particle moving in a straight line is shown in figure. During the interval OA, AB, BC and CD, the acceleration of the particle is OA AB BC CD

A

OA-+, AB-○, BC-+, CD-+

B

OA-+, AB-○, BC-+, CD-○

C

OA-+, AB-○, BC-−, CD-+

D

OA-−, AB-○, BC-−, CD-○

Question 42: Palette 42/135

Errorless MNR 1986 MCQ

A man in a balloon rising vertically with an acceleration of $4.9 \, m/sec^{2}$ releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is $(g = 9.8 \, m/sec^{2})$

A

14.7 m

B

19.6 m

C

9.8 m

D

24.5 m

Question 43: Palette 43/135

Errorless NCERT 1982 MCQ

A point moves with uniform acceleration and $v_{1}, v_{2}$ and $v_{3}$ denote the average velocities in the three successive intervals of time $t_{1}, t_{2}$ and $t_{3}$ . Which of the following relations is correct

A

$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}-t_{2}):(t_{2}+t_{3})$

B

$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}+t_{2}):(t_{2}+t_{3})$

C

$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}-t_{2}):(t_{1}-t_{3})$

D

$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}-t_{2}):(t_{2}-t_{3})$

Question 44: Palette 44/135

Errorless NCERT 1981 MCQ

A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time t/2 sec

A

At h/2 from the ground

B

At h/4 from the ground

C

Depends upon mass and volume of the body

D

At $3h / 4$ from the ground

Question 45: Palette 45/135

Errorless NCERT 1971 MCQ

The displacement versus time graph for a body moving in a straight line in shown in figure. Which of the following regions represents the motion when no force is acting on the body

A

ab

B

bc

C

cd

D

de

Question 46: Palette 46/135

Errorless IIT-JEE 1970 MCQ

A lift is going up. The variation in the speed of the lift is as given in the graph. What is height to which the lift takes the passenger

A

3.6 m

B

28.8 m

C

36.0 m

D

Cannot be calculated from the above graph

Question 47: Palette 47/135

Errorless MCQ

A boy stops after travelling 3 km towards east and then goes 4 km towards north along a plane road. The resultant displacement of the boy is

A

7 km

B

4 km

C

5 km

D

15 km

Question 48: Palette 48/135

Errorless MCQ

If the displacement of a particle is zero, then what can we say about its distance covered

A

It must be zero

B

It cannot be zero

C

It is negative

D

It may or may not be zero

Question 49: Palette 49/135

Errorless MCQ

The location of a particle has changed. What can we say about the displacement and the 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 50: Palette 50/135

Errorless MCQ

A particle moves along a circular arc of radius $R$ making an angle of $\theta$ at centre. The magnitude of displacement is

A

$2R\sin \theta / 2$

B

$2R\sin \theta$

C

$R\sin \theta / 2$

D

$R\sin \theta$

Question 51: Palette 51/135

Errorless MCQ

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

A

S / 5

B

2S / 5

C

S / 2 + S / 3

D

None of the above

Question 52: Palette 52/135

Errorless MCQ

When a particle moves with uniform velocity, which of the following relations are correct (I) Average speed = average velocity (II) Instantaneous speed = instantaneous velocity (III) Distance covered = magnitude of displacement

A

I, II, III

B

I, II

C

II, III

D

I, III

Question 53: Palette 53/135

Errorless MCQ

When a particle moves with variable velocity, which of the following statements are not correct (I) Average speed = average velocity (II) Instantaneous speed = instantaneous velocity (III) Distance covered = magnitude of displacement

A

I, II, III

B

I, II

C

II, III

D

I, III

Question 54: Palette 54/135

Errorless MCQ

A particle moves along the sides AB, BC, CD of a square of side 25 m with a velocity of $15 \, ms^{-1}$ . Its average velocity is

A

$15ms^{-1}$

B

$10ms^{-1}$

C

$7.5ms^{-1}$

D

$5ms^{-1}$

Question 55: Palette 55/135

Errorless MCQ

A body has speed V, 2V and 3V in first 1/3 of distance S, seconds 1/3 of S and third 1/3 of S respectively. Its average speed will be

A

V

B

2V

C

$\frac{18}{11}$ V

D

$\frac{11}{18}$ V

Question 56: Palette 56/135

Errorless MCQ

A particle moving in a straight line covers half the distance with speed of 3 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 [IIT-JEE 199]

A

4.0 m/s

B

5.0 m/s

C

5.5 m/s

D

4.8 m/s

Question 57: Palette 57/135

Errorless MCQ

If the body covers one-third distance at speed $v_{1}$ , next one third at speed $v_{2}$ and last one third at speed $v_{3}$ , then average speed will be

A

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

B

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

C

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

D

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

Question 58: Palette 58/135

Errorless MCQ

The displacement of the 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

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

C

$kb e^{-bt}$

D

None of these

Question 59: Palette 59/135

Errorless MCQ

The displacement of a particle is given by $\sqrt{x} = t + 1$ . Which of the following statements about its velocity is true

A

It is zero

B

It is constant but not zero

C

It increases with time

D

It decreases with time

Question 60: Palette 60/135

Errorless MCQ

The correct statement from the following is

A

A body having zero velocity will not necessarily have zero acceleration

B

A body having zero velocity will necessarily have zero acceleration

C

A body having uniform speed can have only uniform acceleration

D

A body having non-uniform velocity will have zero acceleration

Question 61: Palette 61/135

Errorless MCQ

What is the angle between instantaneous displacement and acceleration during the retarded motion

A

Zero

B

$\frac{\pi}{4}$

C

$\frac{\pi}{2}$

D

$\pi$

Question 62: Palette 62/135

Errorless MCQ

The acceleration of a particle starting from rest, varies with time according to the relation $A = -a\omega^2 \sin \omega t$ . The displacement of this particle at a time $t$ will be

A

$-\frac{1}{2}\left(a\omega^2 \sin \omega t\right)t^2$

B

$a\omega \sin \omega t$

C

$a\omega \cos \omega t$

D

$a \sin \omega t$

Question 63: Palette 63/135

Errorless 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

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

B

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

C

$12 \, m/s^{2}$

D

$14 \, m/s^{2}$

Question 64: Palette 64/135

Errorless MCQ

A car dealcelerates at a constant rate during a period commencing at $t = 0$ . Which of the displacement time graphs represents the displacement of the car

A

B

C

D

Question 65: Palette 65/135

Errorless MCQ

Which of the following can not be the distance time graph

A

B

C

D

Question 66: Palette 66/135

Errorless MCQ

Which of the following displacement time graphs is not possible

A

B

C

D

Question 67: Palette 67/135

Errorless MCQ

The $x - t$ graph in figure represents

A

Constant velocity

B

Velocity of the body continuously changing

C

Instantaneous velocity

D

The body travels with constant speed up to time $t_{1}$ and then stops

Question 68: Palette 68/135

Errorless MCQ

The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is

A

60 m

B

55 m

C

25 m

D

30 m

Question 69: Palette 69/135

Errorless MCQ

A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed in t, then the maximum velocity acquired by the car is

A

$\left(\frac{\alpha^{2}+\beta^{2}}{\alpha\beta}\right)t$

B

$\left(\frac{\alpha^{2}-\beta^{2}}{\alpha\beta}\right)t$

C

$\frac{(\alpha+\beta)t}{\alpha\beta}$

D

$\frac{\alpha\beta t}{\alpha+\beta}$

Question 70: Palette 70/135

Errorless MCQ

A rocket is projected vertically upwards, whose velocity-time graph is shown in fig. The maximum height reached by the rocket is

A

1 km

B

10 km

C

20 km

D

60 km

Question 71: Palette 71/135

Errorless MCQ

In the above problem the mean velocity of rocket in reaching the maximum height will be

A

100 m/s

B

50 m/s

C

500 m/s

D

25/3 m/s

Question 72: Palette 72/135

Errorless MCQ

In the above problem the acceleration of rocket will be

A

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

B

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

C

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

D

$250 \, m/s^{2}$

Question 73: Palette 73/135

Errorless MCQ

The figure shows the velocity of a particle plotted against time t

A

The displacement of the particle is zero

B

The particle changes its direction of motion at some point

C

The initial and final speeds of the particle are same

D

All of the above statements are correct

Question 74: Palette 74/135

Errorless MCQ

The v-t plot of a moving object is shown in the figure. The average velocity of the object during the first 10 seconds is

A

0

B

$2.5 \, ms^{-1}$

C

$5 \, ms^{-1}$

D

$2 \, ms^{-1}$

Question 75: Palette 75/135

Errorless MCQ

Which of the following velocity time graphs is possible.

A

B

C

D

Question 76: Palette 76/135

Errorless MCQ

The graph below shows the velocity versus time graph for a body Which of the following graphs represents the corresponding acceleration versus time graphs

A

B

C

D

Question 77: Palette 77/135

Errorless MCQ

The acceleration-time graph for a body is shown in the following graph. Which of the following graphs would probably represent the velocity of the body plotted against time

A

B

C

D

Question 78: Palette 78/135

Errorless MCQ

A particle is moving in such a way that its displacement is related with time by the equation $x = (10 - 4t + 6t^{2})m$ . The diagram showing variation of velocity of particle with time is

A

B

C

D

Question 79: Palette 79/135

Errorless MCQ

A particle moves along a straight line path. After some time it comes to rest. The motion is with constant acceleration whose direction with respect to the direction of velocity is

A

Positive throughout motion

B

Negative throughout motion

C

First positive then negative

D

First negative then positive

Question 80: Palette 80/135

Errorless MCQ

A bus is moving with a velocity $10 \, ms^{-1}$ on a straight road. A scooterist wishes to overtake the bus in 100 s. If, the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus

A

$50 \, ms^{-1}$

B

$40 \, ms^{-1}$

C

$30 \, ms^{-1}$

D

$20 \, ms^{-1}$

Question 81: Palette 81/135

Errorless MCQ

The velocity acquired by a body moving with uniform acceleration is $30ms^{-1}$ in 2 seconds and $60ms^{-1}$ in four seconds. The initial velocity is

A

$4ms^{-1}$

B

$0ms^{-1}$

C

$2ms^{-1}$

D

$10ms^{-1}$

Question 82: Palette 82/135

Errorless MCQ

An engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartment with velocity v. The middle point of the train passes past the same pole with a velocity of

A

$\sqrt{\frac{v^{2}-u^{2}}{2}}$

B

$\sqrt{\frac{v^{2}+u^{2}}{2}}$

C

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

D

$\frac{u+v}{2}$

Question 83: Palette 83/135

Errorless MCQ

A uniformly accelerated body passes two points P and Q with speeds of 10 m/s and 20 m/s respectively. If O is mid-point of P and Q then speed of O will be

A

15.0 m/s

B

15.8 m/s

C

16.5 m/s

D

14.2 m/s

Question 84: Palette 84/135

Errorless MCQ

A particle starts from rest and moving with constant acceleration covers a distance $x_{1}$ in the 3rd second and $x_{2}$ in the 5th second. The ratio $x_{1}/x_{2}=$

A

3/5

B

5/9

C

9/25

D

25/81

Question 85: Palette 85/135

Errorless MCQ

A particle starts moving along a straight line path with a velocity $10 \, ms^{-1}$ . After 5 seconds, the distance of the particle from the starting point is 50 m. Which of the following statements about the nature of motion of the particle are correct? I. The motion may be with constant acceleration. II. The motion is continuously with constant velocity. III. The motion is continuously retarded IV. The motion may be first accelerated and then retarded

A

I, III

B

II, IV

C

I, II

D

III, IV

Question 86: Palette 86/135

Errorless 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 87: Palette 87/135

Errorless MCQ

A body is moving from rest under constant acceleration and let $S_{1}$ be the displacement in the first $(p - 1)\mathrm{sec}$ and $S_{2}$ be the displacement in the first $p\mathrm{sec}$ . The displacement in $(p^2 - p + 1)^{th}\mathrm{sec}$ will be

A

$S_{1} + S_{2}$

B

$S_{1}S_{2}$

C

$S_{1} - S_{2}$

D

$S_{1} / S_{2}$

Question 88: Palette 88/135

Errorless MCQ

A thief is running away on a straight road in jeep moving with a speed of $9 \, ms^{-1}$ . A police man chases him on a motor cycle moving at a speed of $10 \, ms^{-1}$ . If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police to catch the thief 126 Motion in one dimension

A

1 s

B

19 s

C

90 s

D

100 s

Question 89: Palette 89/135

Errorless MCQ

A car $A$ is travelling on a straight level road with a uniform speed of $60 \, km/h$ . It is followed by another car $B$ which is moving with a speed of $70 \, km/h$ . When the distance between them is $2.5 \, km$ , the car $B$ is given a deceleration of $20 \, km/h^2$ . After how much time will $B$ catch up with $A$

A

$1 \, hr$

B

$1/2 \, hr$

C

$1/4 \, hr$

D

$1/8 \, hr$

Question 90: Palette 90/135

Errorless MCQ

Two cars A and B are travelling in the same the direction with velocities $v_{1}$ and $v_{2}(v_{1}>v_{2})$ . When the car A is at a distance d ahead of the car B, the driver of the car A applies the brake producing a uniform retardation a there will be no collision when

A

$d < \frac{(v_{1} - v_{2})^{2}}{2a}$

B

$d < \frac{(v_{1}^{2} - v_{2}^{2})}{2a}$

C

$d > \frac{(v_{1} - v_{2})^{2}}{2a}$

D

$d > \frac{v_{1}^{2} - v_{2}^{2}}{2a}$

Question 91: Palette 91/135

Errorless MCQ

The displacement x of a particle in time t is given by $10t^{2}-4t-x=0$ . Where x is in metre and t in second. The distance covered by the body in $4^{th}$ second of motion

A

31 m

B

39.5 m

C

66 m

D

75 m

Question 92: Palette 92/135

Errorless MCQ

The speed of a body moving with uniform acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

A

$\sqrt{3}u$

B

$\sqrt{5}u$

C

$\sqrt{11}u$

D

$\sqrt{7}u$

Question 93: Palette 93/135

Errorless MCQ

Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed $10 \, m/s$ . If their acceleration are $0.3 \, m/s^{2}$ and $0.2 \, m/s^{2}$ respectively, then the time they take to pass each other will be

A

5 s

B

10 s

C

15 s

D

20 s

Question 94: Palette 94/135

Errorless MCQ

If the distances covered by an accelerated body during the $l^{th}$ , $m^{th}$ and $n^{th}$ seconds are a, b and c respectively, then the correct relation is

A

$a(m-n)+b(n-l)+c(l-m)=0$

B

$l(b+c)+m(c+a)+n(a+b)=0$

C

$al+bm+cn=0$

D

None of these is true

Question 95: Palette 95/135

Errorless MCQ

Two trains, one travelling at 90 m/s and the other travelling at 120 m/s, are moving towards each other on the same track. When they are 11 km apart, both drivers simultaneously apply brakes. If the brakes decelerate each train at the rate of $3 \, m/s^{2}$ , then the distance travelled by the first train is.

A

1350 m

B

2400 m

C

4740 m

D

8870 m

Question 96: Palette 96/135

Errorless MCQ

In the above problem, the distance travelled by the second train is

A

$1350m$

B

$2400m$

C

$3740m$

D

$8870m$

Question 97: Palette 97/135

Errorless MCQ

In the above problem whether a collision will take place or not

A

Collision will take place

B

There shall be no collision

C

Collision may not take place

D

None of these

Question 98: Palette 98/135

Errorless MCQ

A body starts from rest with uniform acceleration. If its velocity after n second is $\nu$ , then its displacement in the last two seconds is

A

$\frac{2\nu(n+1)}{n}$

B

$\frac{\nu(n+1)}{n}$

C

$\frac{\nu(n-1)}{n}$

D

$\frac{2\nu(n-1)}{n}$

Question 99: Palette 99/135

Errorless MCQ

Two particles move in a straight line towards each other with initial velocities $\nu_{1}$ and $\nu_{2}$ and retardation $a_{1}$ and $a_{2}$ towards each other. The maximum initial separation between the two particles so that they may meet must be

A

$\frac{\left(\nu_{1}+\nu_{2}\right)}{2\left(a_{1}+a_{2}\right)}$

B

$\frac{\left(\nu_{1}+\nu_{2}\right)^{2}}{2\left(a_{1}+a_{2}\right)}$

C

$\frac{\left(\nu_{1}+\nu_{2}\right)}{2a_{1}a_{2}}$

D

$\frac{\left(\nu_{1}+\nu_{2}\right)}{2\left(a_{1}+a_{2}\right)^{2}}$

Question 100: Palette 100/135

Errorless MCQ

A point starts moving in a straight line with a certain acceleration. At a time t after beginning of motion the acceleration suddenly becomes retardation of the same value. The time in which the point returns to the initial point is

A

$\sqrt{2t}$

B

$(2 + \sqrt{2})t$

C

$\frac{t}{\sqrt{2}}$

D

Cannot be predicted unless acceleration is given

Question 101: Palette 101/135

Errorless MCQ

A particle is moving in a straight line and passes through a point O with a velocity of $6 \, ms^{-1}$ . The particle moves with a constant retardation of $2 \, ms^{-2}$ for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

A

3s

B

8s

C

Never

D

4s

Question 102: Palette 102/135

Errorless MCQ

A bird flies for 4 s with a velocity of $\left| t - 2 \right| m / s$ in a straight line, where t = time it seconds. It covers a distance of

A

2 m

B

4 m

C

6 m

D

8 m

Question 103: Palette 103/135

Errorless MCQ

A particle, initially at rest, starts moving in a straight line with an acceleration $a = 6t + 4m/s^{2}$ . The distance covered by it in 3 s is

A

30 m

B

60 m

C

45 m

D

15 m

Question 104: Palette 104/135

Errorless MCQ

The Initial velocity of a particle is $u$ (at $t = 0$ ) and the acceleration $f$ is given by $a t$ . Which of the following relation is valid

A

$v = u + a t^2$

B

$v = u + a \frac{t^2}{2}$

C

$v = u + a t$

D

$v = u$

Question 105: Palette 105/135

Errorless MCQ

The velocity of a particle is dependent on the time as $v = k(t - 1)$ where $k = 2 \, m/s^{2}$ . the distance covered in first three seconds will be

A

18 m

B

5 m

C

3 m

D

6 m

Question 106: Palette 106/135

Errorless MCQ

A particle is projected with velocity $v_{0}$ along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e., $a = \alpha x^{2}$ . The distance at which the particle stops is

A

$\sqrt{\frac{3v_{0}}{2\alpha}}$

B

$\left(\frac{3v_{o}}{2\alpha}\right)^{\frac{1}{3}}$

C

$\sqrt{\frac{3v_{0}^{2}}{2\alpha}}$

D

$\left(\frac{3v_{0}^{2}}{2\alpha}\right)^{\frac{1}{3}}$

Question 107: Palette 107/135

Errorless MCQ

A ball is dropped from top of a tower of 100m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50 m/s ( $g = 10 \, m / s^{2}$ ). They will cross each other after

A

1s

B

2s

C

3s

D

4s

Question 108: Palette 108/135

Errorless MCQ

A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initial velocity (u) of the ball and for how much time (T) it remains in the air $[g = 10m/s^{2}]$

A

u = 10 m/s, T = 2s

B

u = 10 m/s, T = 4s

C

u = 20 m/s, T = 2s

D

u = 20 m/s, T = 4s

Question 109: Palette 109/135

Errorless MCQ

A balloon starts rising from the ground with an acceleration of $1.25 \, m/s^{2}$ after 8s, a stone is released from the balloon. The stone will ( $g = 10 \, m/s^{2}$ )

A

Reach the ground in 4 second released

B

Begin to move down after being

C

Have a displacement of 50 m

D

Cover a distance of 40 m in reaching the ground

Question 110: Palette 110/135

Errorless MCQ

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is $30^{\circ}$ ) is

A

$\frac{1}{2}$ sec

B

2 sec

C

4 sec

D

1 sec

Question 111: Palette 111/135

Errorless MCQ

A ball is dropped downwards. After 1 second another ball is dropped downwards from the same point. What is the distance between them after 3 seconds

A

25 m

B

20 m

C

50 m

D

9.8 m

Question 112: Palette 112/135

Errorless MCQ

A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of $1m$ each will then be

A

All equal, being equal to $\sqrt{2 / g}$ second

B

In the ratio of square roots of the integers 1, 2, 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 reciprocal of the square roots of the integers i.e. $\frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{4}}$

Question 113: Palette 113/135

Errorless MCQ

A rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \, m/sec^2$ . If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be

A

245 m

B

490 m

C

980 m

D

735 m

Question 114: Palette 114/135

Errorless MCQ

A body is slipping from an inclined plane of height h and length l. If the angle of inclination is $\theta$ , the time taken by the body to come from the top to the bottom of this inclined plane is

A

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

B

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

C

$\frac{1}{\sin\theta}\sqrt{\frac{2h}{g}}$

D

$\sin\theta\sqrt{\frac{2h}{g}}$

Question 115: Palette 115/135

Errorless MCQ

A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

A

$\frac{2\sqrt{gR}}{g\cos\theta}$

B

$2\sqrt{gR}\cdot\frac{\cos\theta}{g}$

C

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

D

$\frac{gR}{\sqrt{g\cos\theta}}$

Question 116: Palette 116/135

Errorless MCQ

Two particles one 0.98 m vertically above the other are released simultaneously. They fall under gravity $(g = 9.8 \, m/s^{2})$ . The separation between the two particles after 2 s will be

A

0.49 m

B

4.9 m

C

0.98 m

D

19.6 m

Question 117: Palette 117/135

Errorless MCQ

Two balls are dropped from different heights. One ball is dropped 2 sec after the other ball. If both balls reach the ground simultaneously after 5 sec of dropping the first ball the difference of initial heights of the two balls will be $(g = 9.8 \, m/s^{2})$

A

58.8 v

B

78.4 m

C

98 m

D

117.6 m

Question 118: Palette 118/135

Errorless MCQ

A balloon is moving upwards with a constant velocity of 5 m/s. A stone is dropped from it. If at the moment of dropping the stone the balloon is at height of 50 m, then when the stone will hit the ground, at that time the height of the balloon will be $(g = 10 \, m / s^{2})$

A

68.3 m

B

63.5 m

C

75.5 m

D

88.7 m

Question 119: Palette 119/135

Errorless MCQ

A stone thrown upwards with a velocity u reaches up to a height h. If the initial velocity is 2u the height attained would be

A

2h

B

4h

C

8h

D

16h

Question 120: Palette 120/135

Errorless MCQ

A person throws balls into the air one after the other at an interval of one second. The next ball is thrown when the velocity of the ball thrown earlier is zero. To what height the ball rise (Take $g = 10 \, m / s^{-2}$ )

A

5 m

B

10 m

C

25 m

D

40 m

Question 121: Palette 121/135

Errorless MCQ

A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

A

$\vec{v}/2$ and v/2

B

o and v/2

C

o and o

D

$\vec{v}/2$ and o

Question 122: Palette 122/135

Errorless MCQ

Two balls A and B are simultaneously thrown. A is thrown from ground level with a velocity of $20 \, ms^{-1}$ in the upward direction and B is thrown from a height of 40 m in the downward direction with same velocity. Where will the two balls meet

A

15 m

B

25 m

C

35 m

D

45 m

Question 123: Palette 123/135

Errorless MCQ

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time

A

$\sqrt{\frac{h}{8g}}$

B

$\sqrt{8gh}$

C

$\sqrt{2gh}$

D

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

Question 124: Palette 124/135

Errorless MCQ

A body is released from a height towards the ground level. Just after one second another body is released from same height. The distance between two bodies just after two seconds after the release of second body will be

A

4.9 m

B

9.8 m

C

19.6 m

D

24.5 m

Question 125: Palette 125/135

Errorless MCQ

A stone falls from the top of the tower in 8 sec. How much time will it take to cover the first quarter of the distance starting from the top

A

4 sec

B

2 sec

C

1 sec

D

None of these

Question 126: Palette 126/135

Errorless MCQ

Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown straight up, B is thrown straight down and C is thrown horizontally. They hit the ground with speeds $\upsilon_{A}$ , $\upsilon_{B}$ and $\upsilon_{C}$ respectively, then Motion in one dimension 131

A

$\upsilon_{A} = \upsilon_{B} = \upsilon_{C}$

B

$\upsilon_{A} > \upsilon_{B} > \upsilon_{C}$

C

$\nu_{A} = \nu_{B} > \nu_{C}$

D

$\upsilon_{A} > \upsilon_{B} = \upsilon_{C}$

Question 127: Palette 127/135

Errorless 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, 25 and 15 m

B

30, 20 and 10 m

C

20, 10 and 5 m

D

40, 30 and 20 m

Question 128: Palette 128/135

Errorless MCQ

A ball is dropped from the top of the tower of height $h$ . It covers a distance of $h / 2$ in the last second of its motion. How long does the ball remain in air (Take $g = 10ms^{-2}$ )

A

$\sqrt{2}s$

B

$(2 + \sqrt{2})s$

C

$2s$

D

None of the above

Question 129: Palette 129/135

Errorless MCQ

A body is dropped form height $h$ . If $t_1$ and $t_2$ be the times in covering first half and next half distances respectively, then the correct relation is

A

$t_1 = t_2$

B

$t_1 = 2t_2$

C

$t_1 = \frac{t_2}{\sqrt{2} - 1}$

D

$t_1 = 4t_2$

Question 130: Palette 130/135

Errorless MCQ

A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

A

$4\sqrt{\frac{h}{g}}$

B

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

C

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

D

$\sqrt{\frac{g}{h}}$

Question 131: Palette 131/135

Errorless MCQ

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

A

$\frac{v}{g} + \frac{2hg}{\sqrt{2}}$

B

$\frac{v}{g}\left[1 - \sqrt{1 + \frac{2h}{g}}\right]$

C

$\frac{v}{g}\left[1 + \sqrt{1 + \frac{2gh}{v^{2}}}\right]$

D

$\frac{v}{g}\left[1 + \sqrt{v^{2} + \frac{2g}{h}}\right]$

Question 132: Palette 132/135

Errorless MCQ

Two bodies are thrown simultaneously from a tower with same initial velocity $v_{0}$ : one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is

A

$2v_{0}t + \frac{1}{2}gt^{2}$

B

$2v_{0}t$

C

$v_{0}t + \frac{1}{2}gt^{2}$

D

$v_{0}t$

Question 133: Palette 133/135

Errorless MCQ

A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is

A

50 m

B

75 m

C

100 m

D

125 m

Question 134: Palette 134/135

Errorless MCQ

A particle is projected upwards. The times corresponding to height h while ascending and while descending are $t_{1}$ and $t_{2}$ respectively. The velocity of projection will be

A

$gt_{1}$

B

$gt_{2}$

C

$g(t_{1} + t_{2})$

D

$\frac{g(t_{1} + t_{2})}{2}$

Question 135: Palette 135/135

Errorless MCQ

A projectile is fired vertically upwards with an initial velocity $u$ . After an interval of $T$ seconds a second projectile is fired vertically upwards, also with initial velocity $u$ .

A

They meet at time $t = \frac{u}{g}$ and at a height $\frac{u^2}{2g} + \frac{gT^2}{8}$

B

They meet at time $t = \frac{u}{g} + \frac{T}{2}$ and at a height $\frac{u^2}{2g} + \frac{gT^2}{8}$

C

They meet at time $t = \frac{u}{g} + \frac{T}{2}$ and at a height $\frac{u^2}{2g} - \frac{gT^2}{8}$

D

They never meet