Question 1: Palette 1/125

Objective NEET 2019 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 is shot with the same velocity, it can travel $x_{2}$ distance. Then, $x_{1}:x_{2}$ will be

A

$\sqrt{2}:1$

B

$1:\sqrt{3}$

C

$1:2\sqrt{3}$

D

$1:\sqrt{2}$

Question 2: Palette 2/125

Objective NEET (Odisha) 2019 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 200 m with the same velocity of $25 \, ms^{-1}$ . When and where will the two bullets collides? (Take, $g = 10 \, ms^{-2}$ )

A

After 2s at a height of 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 3: Palette 3/125

Objective AIIMS 2018 MCQ

Assertion The maximum height of projectile is always 25% of the maximum range. Reason For maximum range, projectile should be projected at 90°.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 4: Palette 4/125

Objective JIPMER 2018 MCQ

What is the range of a projectile thrown with velocity $98 \, ms^{-1}$ with angle $30^{\circ}$ from horizontal?

A

$490\sqrt{3} \, m$

B

$245\sqrt{3} \, m$

C

$980\sqrt{3} \, m$

D

$100 \, m$

Question 5: Palette 5/125

Objective AIIMS 2017 MCQ

Assertion: When $\theta = 45^{\circ}$ or $135^{\circ}$ , the value of $R$ remains the same, only the sign changes. Reason: $R = \frac{u^{2} \sin 2\theta}{g}$

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 6: Palette 6/125

Objective JIPMER 2017 MCQ

The x and y-coordinates of a particle moving in a plane are given by $x(t) = a \cos(pt)$ and $y(t) = b \sin(pt)$ , where a, b (< a) and p are positive constants of appropriate dimensions and t is time. Then, which of the following is not true?

A

The path of the particle is an ellipse.

B

Velocity and acceleration of the particle are perpendicular to each other at $t = \frac{\pi}{2p}$ .

C

Acceleration of the particle is always directed towards a fixed point.

D

Distance travelled by the particle in time interval between t = 0 and $t = \frac{\pi}{2p}$ is a.

Question 7: Palette 7/125

Objective NEET 2016 MCQ

A particle moves, so that its position vector is given by $r = \cos \omega t \hat{x} + \sin \omega t \hat{y}$ , where $\omega$ is a constant. Which of the following is true?

A

Velocity and acceleration both are parallel to $\mathbf{r}$ .

B

Velocity is perpendicular to r and acceleration is directed towards to origin.

C

Velocity is perpendicular to r and acceleration is directed away from the origin.

D

Velocity and acceleration both are perpendicular to r.

Question 8: Palette 8/125

Objective AIIMS 2015 MCQ

A particle is projected with an angle of projection $\theta$ to the horizontal line passing through the points $(P, Q)$ and $(Q, P)$ referred to horizontal and vertical axes (can be treated as X-axis and Y-axis, respectively). The angle of projection can be given by

A

$\tan^{-1}\left[\frac{P^2 + PQ + Q^2}{PQ}\right]$

B

$\tan^{-1}\left[\frac{P^2 + Q^2 - PQ}{PQ}\right]$

C

$\tan^{-1}\left[\frac{P^2 + Q^2}{2PQ}\right]$

D

$\sin^{-1}\left[\frac{P^2 + Q^2 + PQ}{2PQ}\right]$

Question 9: Palette 9/125

Objective EAMCET 2015 MCQ

An object is thrown towards the tower which is at a horizontal distance of 50 m with an initial velocity of $10 \, ms^{-1}$ and making an angle $30^{\circ}$ with the horizontal. The object hits the tower at certain height. The height from the bottom of the tower, where the object hits the tower is (Take, $g = 10 \, ms^{-2}$ )

A

$\frac{50}{\sqrt{3}} \left[ 1 - \frac{10}{\sqrt{3}} \right] \, m$

B

$\frac{50}{3} \left[ 1 - \frac{10}{\sqrt{3}} \right] \, m$

C

$\frac{100}{\sqrt{3}} \left[ 1 - \frac{10}{\sqrt{3}} \right] \, m$

D

$\frac{100}{3} \left[ 1 - \frac{10}{\sqrt{3}} \right] \, m$

Question 10: Palette 10/125

Objective Kerala CEE 2015 MCQ

The range of a projectile is R when the angle of projection is $40^{\circ}$ . For the same velocity of projection and range, the other possible angle of projection is

A

$45^{\circ}$

B

$50^{\circ}$

C

$60^{\circ}$

D

$40^{\circ}$

E

$90^{\circ}$

Question 11: Palette 11/125

Objective KCET 2015 MCQ

A particle is projected with a velocity v, so that its horizontal range twice the greatest height attained. The horizontal range is

A

$\frac{4v^{2}}{5g}$

B

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

C

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

D

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

Question 12: Palette 12/125

Objective Kerala CEE 2014 MCQ

If the angle of projection of a projector with same initial velocity exceed or fall short of $45^{\circ}$ by equal amount $\alpha$ , then the ratio of horizontal ranges is

A

1 : 2

B

1 : 3

C

1 : 4

D

1 : 1

E

$1 : \sqrt{2}$

Question 13: Palette 13/125

Objective CBSE AIPMT 2014 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 = 5 s. Average velocity vector $(\nu_{\mathrm{av}})$ from t = 0 to 5 s is

A

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

B

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

C

$2(\hat{\mathbf{i}}-\hat{\mathbf{j}})$

D

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

Question 14: Palette 14/125

Objective WB JEE 2014 MCQ

A cricket ball thrown across a field is at heights $h_{1}$ and $h_{2}$ from the point of projection at times $t_{1}$ and $t_{2}$ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is

A

$\left(\frac{h_{1}t_{2}^{2}-h_{2}t_{1}^{2}}{h_{1}t_{1}-h_{2}t_{2}}\right)$

B

$\left(\frac{h_{1}t_{1}^{2}-h_{2}t_{2}^{2}}{h_{1}t_{2}-h_{2}t_{1}}\right)$

C

$\left(\frac{h_{1}t_{2}^{2}-h_{2}t_{1}^{2}}{h_{1}t_{2}-h_{2}t_{1}}\right)$

D

None of these

Question 15: Palette 15/125

Objective UK PMT 2014 MCQ

For an object thrown at $45^{\circ}$ to the horizontal, the maximum height H and horizontal range R are related as

A

R = 16H

B

R = 8H

C

R = 4H

D

R = 2H

Question 16: Palette 16/125

Objective EAMCET 2014 MCQ

A body is projected horizontally from the top of a tower with a velocity of $10 \, ms^{-1}$ . If it hits the ground at an angle of $45^{\circ}$ , then the vertical component of velocity when it hits ground (in $ms^{-1}$ ) is

A

$10\sqrt{2}$

B

$5\sqrt{2}$

C

5

D

10

Question 17: Palette 17/125

Objective EAMCET 2014 MCQ

A body is projected with an angle $\theta$ . The maximum height reached is $h$ . If the time of flight is 4 s and $g = 10 \, \text{ms}^{-2}$ , then value of $h$ is

A

40 m

B

20 m

C

5 m

D

10 m

Question 18: Palette 18/125

Objective NEET 2013 MCQ

The velocity of a projectile at the initial point A is $(2\hat{\mathbf{i}}+3\hat{\mathbf{j}})\mathrm{ms}^{-1}$ . Its velocity (in ms $^{-1}$ ) at point B is

A

$-2\hat{\mathbf{i}} -3\hat{\mathbf{j}}$

B

$-2\hat{\mathbf{i}} +3\hat{\mathbf{j}}$

C

$2\hat{\mathbf{i}} -3\hat{\mathbf{j}}$

D

$2\hat{\mathbf{i}} +3\hat{\mathbf{j}}$

Question 19: Palette 19/125

Objective J & K CET 2013 MCQ

A projectile is thrown with initial velocity $u_{0}$ and angle $30^{\circ}$ with the horizontal. If it remains in the air for 1s, what was its initial velocity?

A

$19.6 \, ms^{-1}$

B

$9.8 \, ms^{-1}$

C

$4.9 \, ms^{-1}$

D

$1 \, ms^{-1}$

Question 20: Palette 20/125

Objective KCET 2013 MCQ

A projectile is projected at $10 \, ms^{-1}$ by making at an angle $60^{\circ}$ to the horizontal. After some time, its velocity makes an angle of $30^{\circ}$ to the horizontal. Its speed at this instant is

A

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

B

$10\sqrt{3}$

C

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

D

$5\sqrt{3}$

Question 21: Palette 21/125

Objective UP CPMT 2013 MCQ

Two particles are projected upwards with the same initial velocity $v_{0}$ in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest point will be

A

$\tan^{2}\theta_{1}$

B

$v_{0}^{2}\sin^{2}\theta_{1}$

C

$v_{0}\sin\theta_{1}$

D

$v_{0}/\cos\theta_{1}$

Question 22: Palette 22/125

Objective J & K CET 2013 MCQ

The velocity vector of the motion described by the position vector of a particle $r = 2t\hat{i} + t^{2}\hat{j}$ is given by

A

$v = 2\hat{i} + 2t\hat{j}$

B

$v = 2t\hat{i} + 2t\hat{j}$

C

$v = t\hat{i} + t^{2}\hat{j}$

D

$v = 2\hat{i} + t^{2}\hat{j}$

Question 23: Palette 23/125

Objective CBSE AIPMT 2012 MCQ

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A

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

B

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

C

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

D

$\theta = 45^{\circ}$

Question 24: Palette 24/125

Objective UP CPMT 2012 MCQ

Trajectories of two projectiles are shown in figure, let $T_{1}$ and $T_{2}$ be the periods and $u_{1}$ and $u_{2}$ are their speeds of projections, then [UP CPMT 2012]

A

$T_{2} > T_{1}$

C

$u_{1} > u_{2}$

B

$T_{1} = T_{2}$

D

$u_{1} < u_{2}$

Question 25: Palette 25/125

Objective BHU 2012 MCQ

If for the same range, the two heights attained are 20 m and 80 m, then the range will be

A

20 m

B

40 m

C

120 m

D

160 m

Question 26: Palette 26/125

Objective BHU 2012 MCQ

A ball thrown by one player reaches the other in 2 s. The maximum height attained by the ball above the point of projection will be (Take, $g = 10 \, ms^{-2}$ )

A

2.5 m

B

5 m

C

7.5 m

D

10 m

Question 27: Palette 27/125

Objective 2000 MCQ

An aeroplane moving horizontally with a speed of $720 \, kmh^{-1}$ drops a food pocket, while flying at a height of 396.9 m. The time taken by a food pocket to reach the ground and its horizontal range is (Take $g = 9.8 \, ms^{-2}$ )

A

3 s and 2000 m

B

5 s and 500 m

C

8 s and 1500 m

D

9 s and 1800 m

Question 28: Palette 28/125

Objective 2000 MCQ

A bullet is to be fired with a speed of $2000 \, ms^{-1}$ to hit a target 200 m away on a level ground. If $g = 10 \, ms^{-2}$ , the gun should be aimed

A

directly at the target

B

5 cm below the target

C

5 cm above the target

D

2 cm above the target

Question 29: Palette 29/125

Objective MCQ

In a two dimensional motion, instantaneous speed $v_{0}$ is a positive constant. Then which of the following are necessarily true? [NCERT Exemplar]

A

The average velocity is not zero at any time.

B

Average acceleration must always vanish.

C

Displacements in equal time intervals are equal.

D

Equal path lengths are traversed in equal intervals.

Question 30: Palette 30/125

Objective MCQ

In a two dimensional motion, instantaneous speed $v_{0}$ is a positive constant. Then, which of the following are necessarily true? [NCERT Exemplar]

A

The acceleration of the particle is zero.

B

The acceleration of the particle is bounded.

C

The acceleration of the particle is necessarily in the plane of motion.

D

The particle must be undergoing a uniform circular motion.

Question 31: Palette 31/125

Objective MCQ

A particle velocity changes from $(2\hat{\mathbf{i}}-3\hat{\mathbf{j}})\mathrm{ms}^{-1}$ to $(3\hat{\mathbf{i}}-2\hat{\mathbf{j}})\mathrm{ms}^{-1}$ in 2 s. If its mass is 1 kg, the acceleration $(\mathrm{ms}^{-2})$ is

A

$-(\hat{\mathbf{i}}+\hat{\mathbf{j}})$

B

$(\hat{\mathbf{i}}+\hat{\mathbf{j}})/2$

C

zero

D

$(\hat{\mathbf{i}}-\hat{\mathbf{j}})/2$

Question 32: Palette 32/125

Objective MCQ

A projectile is thrown at an angle $\theta$ with the horizontal and its range is $R_{1}$ . It is then thrown at an angle $\theta$ with vertical and the range is $R_{2}$ , then

A

$R_{1} = 4R_{2}$

B

$R_{1} = 2R_{2}$

C

$R_{1} = R_{2}$

D

None of these

Question 33: Palette 33/125

Objective MCQ

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component highest first.

A

1, 2, 3, 4

B

2, 3, 4, 1

C

3, 4, 1, 2

D

4, 3, 2, 1

Question 34: Palette 34/125

Objective MCQ

Which of the following is the graph between the height (h) of a projectile and time (t), when it is projected from the ground?

A

B

C

D

Question 35: Palette 35/125

Objective MCQ

Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of the tower?

A

B

C

D

Question 36: Palette 36/125

Objective MCQ

The horizontal range of a projectile fired at an angle of $15^{\circ}$ is 50 m. If it is fired with the same speed at an angle of $45^{\circ}$ , its range will be [NCERT Exemplar]

A

60 m

B

71 m

C

100 m

D

141 m

Question 37: Palette 37/125

Objective MCQ

A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (Take, $g = 10 \, ms^{-2}$ )

A

$2.5 \, ms^{-1}$

B

$5 \, ms^{-1}$

C

$10 \, ms^{-1}$

D

$20 \, ms^{-1}$

Question 38: Palette 38/125

Objective MCQ

Velocity and acceleration of a particle at some instant of time are $\mathbf{v} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}}) \, \text{ms}^{-1}$ and $\mathbf{a} = -(6\hat{\mathbf{i}} + 8\hat{\mathbf{j}}) \, \text{ms}^{-2}$ , respectively. At the same instant particle is at origin, maximum x-coordinate of particle will be

A

1.5 m

B

0.75 m

C

2.25 m

D

4 m

Question 39: Palette 39/125

Objective MCQ

Two paper screens A and B are separated by a distance of 100 m. A bullet pierces A and then B. The hole in B is 10 cm below the hole in A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is

A

$100 \, ms^{-1}$

B

$200 \, ms^{-1}$

C

$600 \, ms^{-1}$

D

$700 \, ms^{-1}$

Question 40: Palette 40/125

Objective MCQ

Two stones having different masses $m_{1}$ and $m_{2}$ are projected at an angle $\alpha$ and $(90^{\circ}-\alpha)$ with same speed from same point. The ratio of their maximum heights is

A

1:1

B

$1:\tan\alpha$

C

$\tan\alpha:1$

D

$\tan^{2}\alpha:1$

Question 41: Palette 41/125

Objective MCQ

Two projectiles A and B are thrown from the same point with velocities v and v/2, respectively. If B is thrown at an angle $45^{\circ}$ with horizontal, what is the inclination of A when their ranges are the same?

A

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

B

$\frac{1}{2}\sin^{-1}\left(\frac{1}{4}\right)$

C

$2\sin^{-1}\left(\frac{1}{4}\right)$

D

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

Question 42: Palette 42/125

Objective MCQ

A particle moves in the XY-plane according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where $k$ and $\alpha$ are positive constants and $t$ is time. The trajectory of the particle is

A

$y = kx$

B

$y = x - \frac{\alpha x^2}{k}$

C

$y = -\frac{ax^2}{k}$

D

$y = \alpha x$

Question 43: Palette 43/125

Objective MCQ

The maximum range of a gun on horizontal terrain is 1 km. If $g = 10 \, ms^{-2}$ , what must be the muzzle velocity of the shell?

A

$400 \, ms^{-1}$

B

$200 \, ms^{-1}$

C

$100 \, ms^{-1}$

D

$50 \, ms^{-1}$

Question 44: Palette 44/125

Objective MCQ

The equation of trajectory of a projectile is $y = \sqrt{3} x - \frac{g}{2} x^2$ , the angle of its projection is

A

$90^\circ$

B

zero

C

$60^\circ$

D

$30^\circ$

Question 45: Palette 45/125

Objective MCQ

A projectile is thrown upward with a velocity $v_{0}$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

A

$v_{0} \sin \alpha$ vertically downward

B

$2v_{0} \sin \alpha$ vertically downward

C

$2v_{0} \sin \alpha$ vertically upward

D

zero

Question 46: Palette 46/125

Objective MCQ

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be

A

20%

B

15%

C

10%

D

5%

Question 47: Palette 47/125

Objective MCQ

A body is projected at an angle of $30^{\circ}$ with the horizontal with momentum p. At its highest point, the magnitude of the momentum is

A

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

B

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

C

p

D

$\frac{p}{2}$

Question 48: Palette 48/125

Objective MCQ

A projectile is fired from ground level at an angle $\theta$ above the horizontal. The elevation angle $\phi$ of the highest point as seen from the launch point is related to $\theta$ by the relation

A

$\tan \phi = \frac{1}{4} \tan \theta$

B

$\tan \phi = \tan \theta$

C

$\tan \phi = \frac{1}{2} \tan \theta$

D

$\tan \phi = 2 \tan \theta$

Question 49: Palette 49/125

Objective MCQ

A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy KE of the ball varies with horizontal displacement x as

A

B

C

D

Question 50: Palette 50/125

Objective MCQ

A body projected with velocity u at projection angle $\theta$ has horizontal range R. For the same velocity and projection angle, its range on the moon surface will be $(g_{\text{moon}} = g_{\text{earth}} / 6)$

A

36R

B

$\frac{R}{36}$

C

$\frac{R}{16}$

D

6R

Question 51: Palette 51/125

Objective MCQ

Three balls of same masses are projected with equal speeds at angle $15^{\circ}$ , $45^{\circ}$ , $75^{\circ}$ , and their ranges are respectively $R_{1}$ , $R_{2}$ and $R_{3}$ , then

A

$R_{1} > R_{2} > R_{3}$

B

$R_{1} < R_{2} < R_{3}$

C

$R_{1} = R_{2} = R_{3}$

D

$R_{1} = R_{3} < R_{2}$

Question 52: Palette 52/125

Objective MCQ

A projectile is thrown with an initial velocity of $(a\hat{\mathbf{i}}+b\hat{\mathbf{j}})\mathrm{ms}^{-1}$ . If the range of the projectile is twice the maximum height reached by it, then

A

a = 2b

B

b = a

C

b = 2a

D

b = 4a

Question 53: Palette 53/125

Objective MCQ

The ratio of the speed of a projectile at the point of projection to the speed at the top of its trajectory is x. The angle of projection with the horizontal is

A

$\sin^{-1}x$

B

$\cos^{-1}x$

C

$\sin^{-1}(1/x)$

D

$\cos^{-1}(1/x)$

Question 54: Palette 54/125

Objective MCQ

A man can throw a stone such that it acquires maximum horizontal range 80 m. The maximum height to which it will rise for the same projectile (in metre) is

A

10

B

20

C

40

D

50

Question 55: Palette 55/125

Objective MCQ

The velocity at the maximum height of a projectile is half of its initial velocity of projection (u). Its range on horizontal plane is

A

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

B

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

C

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

D

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

Question 56: Palette 56/125

Objective MCQ

A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \, ms^{-1}$ and $19.6 \, ms^{-1}$ . It will strike the plane after covering distance of

A

39.2 m

B

19.6 m

C

9.8 m

D

4.9 m

Question 57: Palette 57/125

Objective MCQ

The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw it will be

A

$\frac{h}{2}$

B

h

C

2h

D

3h

Question 58: Palette 58/125

Objective MCQ

Four bodies P, Q, R and S are projected with equal velocities 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 59: Palette 59/125

Objective MCQ

A stone is projected in air. Its time of flight is 3 s and range is 150 m. Maximum height reached by the stone is (Take, $g = 10 \, ms^{-2}$ )

A

37.5 m

B

22.5 m

C

90 m

D

11.25 m

Question 60: Palette 60/125

Objective MCQ

A boy throws a ball with a velocity u at an angle $\theta$ with the horizontal. At the same instant, he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of

A

$u \cos \theta$

B

$u \sin \theta$

C

$u \tan \theta$

D

$u \sec \theta$

Question 61: Palette 61/125

Objective MCQ

Galileo writes that for angle of projection of a projectile at angle $(45^{\circ}-\theta)$ and $(45^{\circ}+\theta)$ , the horizontal ranges described by the projectile are in the ratio of (if $\theta\leq45^{\circ}$ )

A

2:1

B

1:2

C

1:1

D

2:3

Question 62: Palette 62/125

Objective MCQ

If time of flight of a projectile is 10 s. Range is 500 m. The maximum height attained by it will be

A

125 m

B

50 m

C

100 m

D

150 m

Question 63: Palette 63/125

Objective MCQ

A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with velocity v. While rising up the velocity of the mass 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

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

D

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

Question 64: Palette 64/125

Objective MCQ

A stone is thrown at an angle $\theta$ with the horizontal, reaches a maximum height $H$ . Then, the time of flight of stone will be

A

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

B

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

C

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

D

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

Question 65: Palette 65/125

Objective MCQ

A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy KE of the ball varies with height h as

A

B

C

D

Question 66: Palette 66/125

Objective MCQ

For a given velocity, a projectile has the same range R for two angles of projection. If $t_{1}$ and $t_{2}$ are the time of flight in the two cases, then $t_{1}t_{2}$ is equal to

A

$\frac{2R}{g}$

B

$\frac{R}{g}$

C

$\frac{4R}{g}$

D

$\frac{R}{2g}$

Question 67: Palette 67/125

Objective MCQ

A cricket ball is hit for a six by the bat at an angle of $45^{\circ}$ to the horizontal with kinetic energy K. At the highest point, the kinetic energy of the ball is

A

zero

B

K

C

K/2

D

$K/\sqrt{2}$

Question 68: Palette 68/125

Objective MCQ

The equation of motion of a projectile is $y = 12x - \frac{3}{4}x^{2}$ What is the range of the projectile?

A

12 m

B

16 m

C

20 m

D

24 m

Question 69: Palette 69/125

Objective MCQ

A ball of mass m is projected from the ground with an initial velocity u making an angle of $\theta$ with the vertical. What is the change in velocity between the point of projection and the highest point?

A

$u \cos \theta$ downward

B

$u \cos \theta$ upward

C

$u \sin \theta$ upward

D

$u \sin \theta$ downward

Question 70: Palette 70/125

Objective MCQ

The equation of projectile is $Y = \sqrt{3}X - \frac{1}{2} gX^{2}$ . The velocity of projection is

A

$1 \, ms^{-1}$

B

$2 \, ms^{-1}$

C

$3 \, ms^{-1}$

D

$1.2 \, ms^{-1}$

Question 71: Palette 71/125

Objective MCQ

The range of a projectile when launched at an angle $\theta$ is same as when launched at an angle $2\theta$ . What is the value of $\theta$ ?

A

$15^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 72: Palette 72/125

Objective MCQ

A particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to $v$ , where

A

$v = u \cos \theta$

B

$v = u \cos \theta \cos \phi$

C

$v = u \cos \theta \sec \phi$

D

$v = u \sec \theta \cos \phi$

Question 73: Palette 73/125

Objective MCQ

A projectile has the maximum range 500 m. If the projectile is thrown up a smooth inclined plane of $30^{\circ}$ with the same (magnitude) velocity, the distance covered by it along the inclined plane till it stops will be

A

250 m

B

500 m

C

750 m

D

1000 m

Question 74: Palette 74/125

Objective MCQ

A projectile $A$ is thrown at an angle $30^{\circ}$ to the horizontal from point $P$ . At the same time, another projectile $B$ is thrown with velocity $v_{2}$ upwards from the point $Q$ vertically below the highest point $A$ would reach. For $B$ to collide with $A$ , the ratio $\frac{v_{2}}{v_{1}}$ should be

A

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

B

2

C

$\frac{1}{2}$

D

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

Question 75: Palette 75/125

Objective MCQ

A ball is thrown from a point O aiming a target at angle $30^{\circ}$ with the horizontal, so that the ball hits the target at B but the ball hits at point A, a vertical distance h below B. If the initial velocity of the ball is $20 \, ms^{-1}$ and the horizontal distance between O and C is 10 m. Find the value of h.

A

$\frac{g}{6}\mathrm{m}$

B

$\frac{g}{10}\mathrm{m}$

C

$\frac{g}{3}\mathrm{m}$

D

$\frac{g}{12}\mathrm{m}$

Question 76: Palette 76/125

Objective MCQ

A ball is thrown from a point with a speed $v_{0}$ at an angle of projection $\theta$ . From the same point and at the same instant, a person starts running with a constant speed $v_{0}/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

A

Yes, $60^{\circ}$

B

Yes, $30^{\circ}$

C

No

D

Yes, $45^{\circ}$

Question 77: Palette 77/125

Objective MCQ

The initial velocity of a particle of mass 2 kg is $(4\hat{\mathbf{i}} + 4\hat{\mathbf{j}})\ \mathrm{ms}^{-1}$ . A constant force of $-20\hat{\mathbf{j}}\ N$ is applied on the particle. Initially, the particle was at $(0, 0)$ . Find the x-coordinate of the point, where its y-coordinate is again zero.

A

3.2 m

B

6 m

C

4.8 m

D

1.2 m

Question 78: Palette 78/125

Objective MCQ

An object of mass m is projected with a momentum p at such an angle that its maximum height is 1/4th of its horizontal range. Its minimum kinetic energy in its path will be

A

$\frac{p^{2}}{8m}$

B

$\frac{p^{2}}{4m}$

C

$\frac{3p^{2}}{4m}$

D

$\frac{p^{2}}{m}$

Question 79: Palette 79/125

Objective MCQ

The equation of motion of a projectile are given by $x = 36 \, t \, \text{m}$ and $2y = 96 \, t - 9.8 \, t^2 \, \text{m}$ . The angle of projection is

A

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

B

$\sin^{-1} \left( \frac{3}{5} \right)$

C

$\sin^{-1} \left( \frac{4}{3} \right)$

D

$\sin^{-1} \left( \frac{3}{4} \right)$

Question 80: Palette 80/125

Objective MCQ

Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is

A

$45^{\circ}$

B

$60^{\circ}$

C

$30^{\circ}$

D

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

Question 81: Palette 81/125

Objective MCQ

An arrow is shot into air. Its range is 200 m and its time of flight is 5 s. If $g = 10 \, ms^{-2}$ , then horizontal component of velocity and the maximum height will be respectively

A

$20 \, ms^{-1}$ , 62.50 m

B

$40 \, ms^{-1}$ , 31.25 m

C

$80 \, ms^{-1}$ , 62.5 m

D

None of these

Question 82: Palette 82/125

Objective MCQ

A body is projected from the ground with a velocity $\mathbf{v} = (3\hat{\mathbf{i}} + 10\hat{\mathbf{j}}) \, \text{ms}^{-1}$ . The maximum height attained and the range of the body respectively are (Take, $g = 10 \, ms^{-2}$ )

A

5 m and 6 m

B

3 m and 10 m

C

6 m and 5 m

D

3 m and 5 m

Question 83: Palette 83/125

Objective MCQ

A cricket fielder can throw the cricket ball with a speed $v_{0}$ . If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal, what is the effective angle to the horizontal at which the ball is projected in air as seen by a spectator? [NCERT Exemplar]

A

$\tan^{-1}\left(\frac{v_{0}\cos\theta}{u + v_{0}\sin\theta}\right)$

B

$\tan^{-1}\left(\frac{v_{0}\sin\theta}{u + v_{0}\cos\theta}\right)$

C

$\tan^{-1}\left(\frac{u}{v_{0}\cos\theta + v_{0}\sin\theta}\right)$

D

$\tan^{-1}\left(\frac{v_{0}\sin\theta + v_{0}\cos\theta}{u}\right)$

Question 84: Palette 84/125

Objective MCQ

A particle is projected with a velocity of $30 \, ms^{-1}$ , at an angle of $\theta_{0} = \tan^{-1} \left( \frac{3}{4} \right)$ . After 1 s, the particle is moving at an angle $\theta$ to the horizontal, where $\tan\theta$ will be equal to (Take, $g = 10 \, ms^{-2}$ )

A

1

B

2

C

$\frac{1}{2}$

D

$\frac{1}{3}$

Question 85: Palette 85/125

Objective MCQ

A bomber plane moves horizontally with a speed of $500 \, ms^{-1}$ and a bomb released from it, strikes the ground in 10 s. Angle at which it strikes the ground will be (Take, $g = 10 \, ms^{-2}$ )

A

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

B

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

C

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

D

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

Question 86: Palette 86/125

Objective MCQ

Two balls are thrown simultaneously from ground with same velocity of $10 \, ms^{-1}$ but different angles of projection with horizontal. Both balls fall at same distance $5\sqrt{3} \, m$ from point of projection. What is the time interval between balls striking the ground?

A

$(\sqrt{3}-1) \, s$

B

$(\sqrt{3}+1) \, s$

C

$\sqrt{3} \, s$

D

$1 \, s$

Question 87: Palette 87/125

Objective MCQ

A particle moves along a parabolic path $y = -9x^{2}$ in such a way that the x-component of velocity remains constant and has a value $1/3 \, ms^{-1}$ . The acceleration of the particle is

A

$\frac{1}{3} \, ms^{-2}$

B

$3 \, ms^{-2}$

C

$\frac{2}{3} \, ms^{-2}$

D

$2 \, ms^{-2}$

Question 88: Palette 88/125

Objective MCQ

A projectile can have same range from two angles of projection with same initial speed. If $h_{1}$ and $h_{2}$ be the maximum heights, then

A

$R = \sqrt{h_{1} h_{2}}$

B

$R = \sqrt{2 h_{1} h_{2}}$

C

$R = 2\sqrt{h_{1} h_{2}}$

D

$R = 4\sqrt{h_{1} h_{2}}$

Question 89: Palette 89/125

Objective MCQ

A ball is projected from ground with a speed of $20 \, ms^{-1}$ at an angle of $45^{\circ}$ with horizontal. There is a wall of 25 m height at a distance of 10 m from the projection point. The ball will hit the wall at a height of

A

5 m

B

7.5 m

C

10 m

D

12.5 m

Question 90: Palette 90/125

Objective MCQ

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

A

$20\sqrt{2}$ m

B

10 m

C

$10\sqrt{2}$ m

D

20 m

Question 91: Palette 91/125

Objective MCQ

At the height 80 m, an aeroplane is moving with $150 \, ms^{-1}$ . A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? (Take, $g = 10 \, ms^{-2}$ )

A

605.3 m

B

600 m

C

80 m

D

230 m

Question 92: Palette 92/125

Objective MCQ

A ball is projected upwards from the top of a tower with velocity $25 \, ms^{-1}$ making an angle of $30^\circ$ with the horizontal. If the height of the tower is 70 m, after what time from the instant of throwing, will the ball reach the ground? (Take, $g = 10 \, ms^{-2}$ )

A

2 s

B

5 s

C

7 s

D

9 s

Question 93: Palette 93/125

Objective MCQ

From the top of a tower of height 40 m, a ball is projected upwards with a speed of $20 \, ms^{-1}$ at an angle of elevation of $30^\circ$ . The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (Take, $g = 10 \, ms^{-2}$ )

A

2:1

B

3:1

C

3:2

D

1.5:1

Question 94: Palette 94/125

Objective MCQ

The coordinates of a moving particle at any time t are given by x = ct and $y = bt^{2}$ . The speed of the particle is given by

A

$2t\sqrt{b^{2}-c^{2}}$

B

$\sqrt{4b^{2}t^{2}+c^{2}}$

C

$2t(b+c)$

D

$2t(b-c)$

Question 95: Palette 95/125

Objective MCQ

A ball rolls off the edge of a horizontal table top 4 m high. If it strikes the floor at a point 5 m horizontally away from the edge of the table, what was its speed at the instant it left the table?

A

$2.5 \, ms^{-1}$

B

$3.5 \, ms^{-1}$

C

$5.55 \, ms^{-1}$

D

$6.5 \, ms^{-1}$

Question 96: Palette 96/125

Objective MCQ

A ball is thrown from the ground to a wall 3 m high at a distance of 6 m and falls 18 m away from the wall, the angle of projection of ball is

A

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

B

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

C

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

D

$\tan^{-1}\left(\frac{3}{4}\right)$

Question 97: Palette 97/125

Objective MCQ

The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be

A

$(R + H), \frac{H}{2}$

B

$\left(R + \frac{H}{2}\right), 2H$

C

$(R + 2H), H$

D

$(R + H), H$

Question 98: Palette 98/125

Objective MCQ

An object is projected with a velocity of $20 \, ms^{-1}$ making an angle of $45^{\circ}$ with horizontal. The equation for trajectory is $h = Ax - Bx^{2}$ , where h is height, x is horizontal distance, A and B are constants. The ratio A : B is (Take, $g = 10 \, ms^{-2}$ )

A

1:5

B

5:1

C

1:40

D

40:1

Question 99: Palette 99/125

Objective MCQ

If the instantaneous velocity of a particle projected as shown in figure is given by $\mathbf{v} = a\hat{\mathbf{i}} + (b - ct)\hat{\mathbf{j}}$ . 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 100: Palette 100/125

Objective MCQ

Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity g is uniform. If $u_{1}$ and $u_{2}$ be their initial speeds, then the time t after which their velocities are mutually perpendicular is given by

A

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

B

$\frac{\sqrt{u_{1}^{2}+u_{2}^{2}}}{g}$

C

$\frac{\sqrt{u_{1}(u_{1}+u_{2})}}{g}$

D

$\frac{\sqrt{u_{2}(u_{1}+u_{2})}}{g}$

Question 101: Palette 101/125

Objective MCQ

A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80 \, ms^{-1}$ . Its time of flight is T. Its velocity at t = T/4 has a magnitude of nearly

A

$200 \, ms^{-1}$

B

$300 \, ms^{-1}$

C

$100 \, ms^{-1}$

D

None of these

Question 102: Palette 102/125

Objective MCQ

A projectile is thrown with some initial velocity at an angle $\alpha$ to the horizontal. Its velocity when it is at the highest point is $(2/5)^{1/2}$ times the velocity when it is at height half of the maximum height. Find the angle of projection $\alpha$ with the horizontal.

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$37^{\circ}$

Question 103: Palette 103/125

Objective MCQ

A very broad elevator is going up vertically with a constant acceleration of $2 \, ms^{-2}$ . At the instant when its velocity is $4 \, ms^{-1}$ , a ball is projected from the floor of the lift with a speed of $4 \, ms^{-1}$ relative to the floor at an elevation of $30^\circ$ . The time taken by the ball to return the floor is (Take, $g = 10 \, ms^{-2}$ )

A

$\frac{1}{2} \, s$

B

$\frac{1}{3} \, s$

C

$\frac{1}{4} \, s$

D

$1 \, s$

Question 104: Palette 104/125

Objective MCQ

A grasshopper can jump a maximum distance of 1.6 m. How far can it go in 10 s?

A

$5\sqrt{2}$ m

B

$10\sqrt{2}$ m

C

$20\sqrt{2}$ m

D

$40\sqrt{2}$ m

Question 105: Palette 105/125

Objective MCQ

A body of mass 1kg is projected with velocity $50 \, ms^{-1}$ at an angle of $30^{\circ}$ with the horizontal. At the highest point of its path, a force 10 N starts acting on body for 5 s vertically upward besides gravitational force. What is the horizontal range of the body? (Take, $g = 10 \, ms^{-2}$ )

A

$125\sqrt{3} \, m$

B

$200\sqrt{3} \, m$

C

$500 \, m$

D

$250\sqrt{3} \, m$

Question 106: Palette 106/125

Objective MCQ

A projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall at its highest point as shown in the figure. The angle $\theta$ at which the projectile is thrown is given by

A

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

B

$\tan^{-1}\sqrt{3}$

C

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

D

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

Question 107: Palette 107/125

Objective MCQ

A jet aeroplane is flying at a constant height of 2 km with a speed $360 \, kmh^{-1}$ above the ground towards a target and releases a bomb. After how much time, it will hit the target and what will be the horizontal distance of the aeroplane from the target, so that the bomb should hit the target? (Take, $g = 10 \, ms^{-2}$ )

A

10 s, 1 km

B

20 s, 2 km

C

30 s, 3 km

D

40 s, 4 km

Question 108: Palette 108/125

Objective MCQ

Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance 120 m. Which of the following is true?

A

The two balls can never meet

B

The balls can meet, if the ball $B$ is thrown 1 s later

C

The two balls meet at a height of $45\mathrm{m}$

D

None of the above

Question 109: Palette 109/125

Objective MCQ

Two particles are projected from the same point with same speed $u$ at angles of projection $\alpha$ and $\beta$ from horizontal. The maximum heights attained by them are $h_1$ and $h_2$ respectively, $R$ is the range for both. If $t_1$ and $t_2$ are their times of flight respectively, then which amongst the option(s) is/are incorrect?

A

$\alpha + \beta = \frac{\pi}{2}$

B

$R = 4\sqrt{h_1h_2}$

C

$\tan \alpha = \frac{t_1}{t_2} = \sqrt{h_1h_2}$

D

$\tan \alpha = \frac{h_1}{h_2}$

Question 110: Palette 110/125

Objective MCQ

A particle is projected from the ground at an angle $\theta$ with the horizontal with an initial speed u. Time after which velocity vector of the projectile is perpendicular to the initial velocity.

A

$u/g \sin\theta$

B

$u/g \cos\theta$

C

$2u/g \sin\theta$

D

$2u \tan\theta$

Question 111: Palette 111/125

Objective MCQ

A particle is projected from horizontal making an angle of $53^{\circ}$ with initial velocity of $100 \, ms^{-1}$ . The time taken by the particle to make angle $45^{\circ}$ from horizontal is

A

14 s

B

2 s

C

Both

D

None of these

Question 112: Palette 112/125

Objective MCQ

A large number of bullets are fired in all directions with same speed v. What is the maximum area on the ground on which these bullets will spread?

A

$\pi\frac{v^{2}}{g}$

B

$\pi\frac{v^{4}}{g^{2}}$

C

$\pi^{2}\frac{v^{4}}{g^{2}}$

D

$\pi^{2}\frac{v^{2}}{g^{2}}$

Question 113: Palette 113/125

Objective MCQ

For a ground-to-ground projectile, an object is at point A at $t = \frac{T}{3}$ , at point B at $t = \frac{5T}{6}$ and reaches the ground at t = T. The difference in heights between points A and B is

A

$\frac{gT^{2}}{6}$

B

$\frac{gT^{2}}{12}$

C

$\frac{gT^{2}}{18}$

D

$\frac{gT^{2}}{24}$

Question 114: Palette 114/125

Objective MCQ

A cart is moving horizontally along a straight line with a constant speed of $30 \, ms^{-1}$ . A projectile is to be fired from the moving cart in such a way that it will return to the cart (at the same point on cart) after the cart has moved 80 m. At what velocity (relative to the cart) must projectile be fired? (Take, $g = 10 \, ms^{-2}$ )

A

$10 \, ms^{-1}$

B

$\frac{20}{3} \, ms^{-1}$

C

$\frac{40}{3} \, ms^{-1}$

D

$\frac{80}{3} \, ms^{-1}$

Question 115: Palette 115/125

Objective MCQ

Two second after projection, a projectile is travelling in a direction inclined at $30^{\circ}$ with the horizontal. After 1 more second, it is travelling horizontally. Then, (Take, $g = 10 \, ms^{-2}$ )

A

the velocity of projection is $20\sqrt{3} \, ms^{-1}$

B

the angle of projection is $30^{\circ}$ with horizontal

C

Both (a) and (b) are correct

D

Both (a) and (b) are incorrect

Question 116: Palette 116/125

Objective MCQ

A ball rolls off top of a stair way with a horizontal velocity $u \, ms^{-1}$ . If the steps are h metres high and b metres wide, the ball will just hit the edge of nth step, if n equals to

A

$\frac{hu^{2}}{gb^{2}}$

B

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

C

$\frac{2hu^{2}}{gb^{2}}$

D

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

Question 117: Palette 117/125

Objective MCQ

A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of $125 \, ms^{-1}$ over the hill. The canon is located at a distance of 800 m from the foot of hill and can be moved on the ground at a speed of $2 \, ms^{-1}$ , so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? (Take, $g = 10 \, ms^{-2}$ ) [NCERT Exemplar]

A

10 s

B

25 s

C

35 s

D

45 s

Question 118: Palette 118/125

Objective MCQ

Assertion: In case of projectile motion, the magnitude of rate of change of velocity is variable. Reason: In projectile motion, magnitude of velocity first decreases and then increases during the motion.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 119: Palette 119/125

Objective MCQ

Assertion: At highest point of a projectile, dot product of velocity and acceleration is zero. Reason: At highest point, velocity and acceleration are mutually perpendicular.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 120: Palette 120/125

Objective MCQ

Assertion: If a particle is projected vertically upwards with velocity u, the maximum height attained by the particle is $h_{1}$ . The same particle is projected at angle $30^{\circ}$ from horizontal with the same speed u. Now the maximum height is $h_{2}$ . Thus, $h_{1} = 4h_{2}$ . Reason: In first case, v = 0 at highest point and in second case, $v \neq 0$ at highest point.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 121: Palette 121/125

Objective MCQ

A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/s from the same height. The correct statement is

A

both particles will reach at ground simultaneously

B

both particles will reach at ground with same speed

C

particle (A) will reach at ground first with respect to particle (B)

D

particle (B) will reach at ground first with respect to particle (A)

Question 122: Palette 122/125

Objective MCQ

A ball is rolled off the edge of a horizontal table at a speed of $4 \, ms^{-1}$ . It hits the ground after 0.4 s. Which statement given below is true?

A

It hits the ground at a horizontal distance 1.6 m from the edge of the table.

B

The speed with which it hits the ground is $4.0 \, ms^{-1}$ .

C

Height of the table 1m.

D

It hits the ground at an angle of $60^{\circ}$ to the horizontal.

Question 123: Palette 123/125

Objective MCQ

I. In projectile motion, the angle between instantaneous velocity vector and acceleration vector can be anything between 0 to $\pi$ (excluding the limiting case.) II. In projectile motion, acceleration vector is always pointing vertically downwards. (Neglect air friction). Which of the following statement(s) is/are correct?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Question 124: Palette 124/125

Objective MCQ

I. Particle-1 is dropped from a tower and particle-2 is projected horizontal from the same tower, then both the particles reach the ground simultaneously. II. Both the particles strike the ground with different speeds. Which of the following statement(s) is/are correct?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Question 125: Palette 125/125

Objective MCQ

A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in the figure. The horizontal velocity of the block is

A

$\frac{v}{\sin\theta}$

B

$v \sin \theta$

C

$\frac{v}{\cos\theta}$

D

$v\cos \theta$