Question 1: Palette 1/118

Errorless EAMCET 2001 MCQ

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

A

1 : 5

B

5 : 1

C

1 : 40

D

40 : 1

Question 2: Palette 2/118

Errorless IIT-JEE 1999 MCQ

In 1.0 s a particle goes from point A to point B, moving in a semicircle of radius 1.0 m. The magnitude of the average velocity is

A

3.14 m/s

B

2.0 m/s

C

1.0 m/s

D

Zero

Question 3: Palette 3/118

Errorless EAMCET (Med.) 1998 MCQ

A stone is thrown at an angle $\theta$ to the horizontal reaches a maximum height $h$ . The time of flight of the stone is

A

$\sqrt{(2h\sin\theta)/g}$

B

$2\sqrt{(2h\sin\theta)/g}$

C

$2\sqrt{(2h)/g}$

D

$\sqrt{(2h)/g}$

Question 4: Palette 4/118

Errorless RPMT 1998 MCQ

Angular velocity of wheel is 2 radian/second. Calculate the number of rotation of the wheel in 5 second

A

$5 / \pi$

B

$10 / \pi$

C

$10\pi$

D

$20\pi$

Question 5: Palette 5/118

Errorless Manipal 1998 MCQ

A point on the rim of a wheel of diameter 400 cm has a velocity of 16 m/sec. The angular velocity of the wheel is

A

2 rad/sec

B

4 rad/sec

C

6 rad/sec

D

8 rad/sec

Question 6: Palette 6/118

Errorless MP PET/PMT 1998 MCQ

A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4m in a vertical plane. If $g = 10 \, m/s^{2}$ , then the maximum angular velocity of the stone will be

A

4 radians/sec

B

16 radians/sec

C

$\sqrt{21}$ radians/sec

D

2 radians/sec

Question 7: Palette 7/118

Errorless RPET 1997 MCQ

A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be

A

Parabolic

B

Inclined straight line

C

Vertical straight line

D

Horizontal straight line

Question 8: Palette 8/118

Errorless CPMT 1997 MCQ

A projectile has a maximum range of 16 km. At the highest point of its motion, it explodes into two equal masses. One mass drops vertically downwards the horizontal distance covered by the other mass from the time of explosion is

A

8 km

B

16 km

C

24 km

D

32 km

Question 9: Palette 9/118

Errorless CPMT 1996; JIPMER 2001, 02 MCQ

An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

A

1200 m

B

0.33 m

C

3.33 km

D

33 km

Question 10: Palette 10/118

Errorless CPMT 1994 MCQ

A body of mass 4 kg is being rotated with 120 rev. per minute in a horizontal circular path of radius 2m. Its kinetic energy is

A

2 J

B

32 J

C

80 J

D

1263 J

Question 11: Palette 11/118

Errorless SCRA 1994 MCQ

Consider the following statements Assertion (A) : A cyclist always bends inwards while negotiating a curve Reason (R) : By bending he lowers his centre of gravity Of these statements :

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 12: Palette 12/118

Errorless IIT-JEE 1992 MCQ

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$ . The force exerted by the liquid at the other end is

A

$\frac{ML\omega^{2}}{2}$

B

$ML\omega^{2}$

C

$\frac{ML\omega^{2}}{4}$

D

$\frac{ML^{2}\omega^{2}}{2}$

Question 13: Palette 13/118

Errorless IIT 1977 MCQ

The driver of a car travelling at velocity v suddenly see a broad wall in front of him at a distance d. He should

A

Brake sharply

B

Turn sharply

C

(a) and (b) both

D

None of the above

Question 14: Palette 14/118

Errorless MCQ

At the top of the trajectory of a projectile, the directions of its velocity and acceleration are

A

Perpendicular to each other

B

Parallel to each other

C

Inclined to each other at an angle of $45^{\circ}$

D

Antiparallel to each other

Question 15: Palette 15/118

Errorless MCQ

A stone is projected with an initial velocity at an angle to the horizontal. A small piece separates from the stone before the stone reaches its maximum height. Then this piece will

A

Fall to the ground vertically

B

Fly side by side with the parent stone along a parabolic path

C

Fly horizontally initially and will trace a different parabolic path

D

Lag behind the parent stone increasing the distance from it

Question 16: Palette 16/118

Errorless MCQ

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

A

$y = kx$

B

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

C

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

D

$y = \alpha x$

Question 17: Palette 17/118

Errorless MCQ

The equation of motion of a projectile is $y = 12x - \frac{3}{4}x^{2}$ . Given that $g = 10 ms^{-2}$ , what is the range of the projectile

A

12.4 m

B

16 m

C

30.6 m

D

36.0 m

Question 18: Palette 18/118

Errorless MCQ

A particle is moving in a plane with velocity given by $\vec{u} = u_0\hat{i} + (a\omega \cos \alpha t)\hat{j}$ where $\hat{i},\hat{j}$ are unit vectors along $x$ and $y$ axes respectively. The trajectory of the particle if the particle starts from origin at $t = 0$ will be

A

$y = a\sin \left(\frac{\omega x}{u_0}\right)$

B

$y = a\cos \left(\frac{\omega x}{u_0}\right)$

C

$y = \tan x$

D

$y = \cos tx$

Question 19: Palette 19/118

Errorless MCQ

A ball is dropped from the top of a tower in a high speed wind. The wind exerts a steady force on the ball. The path followed by the ball will be

A

Parabola

B

Circular arc

C

Elliptical arc

D

Straight line

Question 20: Palette 20/118

Errorless 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 21: Palette 21/118

Errorless 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 22: Palette 22/118

Errorless MCQ

A boy throws a ball with a velocity $V_{0}$ at an angle $\alpha$ to 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

$V_{0} \cos \alpha$

B

$V_{0} \sin \alpha$

C

$V_{0} \tan \alpha$

D

$\sqrt{V_{0}^{2} \tan \alpha}$

Question 23: Palette 23/118

Errorless MCQ

From the top of a tower 19.6 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

$9.8 \, ms^{-1}$

B

$4.9 \, ms^{-1}$

C

$14.7 \, ms^{-1}$

D

$2.8 \, ms^{-1}$

Question 24: Palette 24/118

Errorless MCQ

When a particle is thrown horizontally, the resultant velocity of the projectile at any time $t$ is given by

A

$gt$

B

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

C

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

D

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

Question 25: Palette 25/118

Errorless 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 $(g = 10 \, ms^{-2})$

A

$2.5 \, ms^{-1}$

B

$5 \, ms^{-1}$

C

$10 \, ms^{-1}$

D

$20 \, ms^{-1}$

Question 26: Palette 26/118

Errorless MCQ

An aeroplane is moving with a horizontal velocity u at a height h above the ground. If a packet is dropped from it the speed of the packet when it reaches the ground will be

A

$(u^{2} + 2gh)^{1/2}$

B

$(2gh)^{1/2}$

C

$(u^{2} - 2gh)^{1/2}$

D

2gh

Question 27: Palette 27/118

Errorless MCQ

A particle is projected with a speed V from a point O making an angle of $30^{\circ}$ with the vertical. At the same instant, a second particle is thrown vertically upwards from a point A. The two particles reach H, the highest point on the parabolic path of particle simultaneously. Then ratio $\frac{V}{v}$ is

A

$3\sqrt{2}$

B

$2\sqrt{3}$

C

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

D

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

Question 28: Palette 28/118

Errorless MCQ

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

A

100 m/sec

B

200 m/sec

C

600 m/sec

D

700 m/sec

Question 29: Palette 29/118

Errorless MCQ

A particle is thrown upward 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, then

A

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

B

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

C

$v = u \cos \theta$

D

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

Question 30: Palette 30/118

Errorless MCQ

Mr. Naveen kicked off a football with an initial speed 19.6 m/s at a projection angle $45^{\circ}$ . A receiver on the goal line 67.4 m away in the direction of the kick starts running to meet the ball at that instant. What must be his speed so that he could catch the ball before hitting the ground

A

2.82 m/s

B

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

C

39.2 m/s

D

10 m/s

Question 31: Palette 31/118

Errorless MCQ

Two balls of same mass are thrown horizontally from the top of a tower in the opposite direction with velocities 3 m/s and 4 m/s. The distance between the balls, when their velocities are mutually perpendicular will be nearest to

A

10 m

B

7 m

C

5 m

D

2.5 m

Question 32: Palette 32/118

Errorless MCQ

A motorcyclist starts from the bottom of a slope of angle $45^{\circ}$ to cross the valley PR as shown in the figure. The width of the valley is 90 m and length of the slope is $80\sqrt{2}m$ . The minimum velocity at point O required to clear the valley will be

A

70 m/s

B

30 m/s

C

50 m/s

D

100 m/s

Question 33: Palette 33/118

Errorless MCQ

From the top of a tower of height h a body of a mass m is projected in the horizontal direction with a velocity v. It falls on the ground at a distance x from the tower. If a body of mass 2 m is projected from the top of another tower of height 2 h in the horizontal direction so that it falls on the ground at a distance 2x from the tower, the horizontal velocity of the second body is

A

2 v

B

$\sqrt{2v}$

C

$\frac{v}{2}$

D

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

Question 34: Palette 34/118

Errorless MCQ

A cricket ball is thrown with a velocity of 15 m/s at an angle of $30^{\circ}$ with the horizontal. The time of flight of the ball will be $(g = 10 \, \text{m/s}^{2})$

A

1.5 s

B

2.5 s

C

3.5 s

D

4.5 s

Question 35: Palette 35/118

Errorless MCQ

If $t_{1}$ be the time taken by a body to clear the top of a building and $t_{2}$ be the time spent in air, then $t_{2}:t_{1}$ will be

A

1:2

B

2:1

C

1:1

D

1:4

Question 36: Palette 36/118

Errorless 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 the highest point

A

11 sec

B

23 sec

C

38 sec

D

51 sec

Question 37: Palette 37/118

Errorless MCQ

Two bullets are fired with horizontal velocities of 50 m/s and 100 m/s from two guns at a height of 19.6 m. Which bullet will strike first

A

First

B

Second

C

Simultaneously

D

None of these

Question 38: Palette 38/118

Errorless MCQ

A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with a speed of 15 $ms^{-1}$ . The time taken by the stone to reach the ground is

A

10 s

B

5 s

C

12 s

D

15 s

Question 39: Palette 39/118

Errorless MCQ

Galileo's experiment showed that if two bodies of unequal masses are dropped from the same height, the time required by them to reach the ground are equal. But if they are thrown vertically upwards with the same initial velocity, the ratio of the time required to reach the ground is equal to

A

The ratio of their masses

B

The inverse of the ratio of their masses

C

One

D

The product of their masses

Question 40: Palette 40/118

Errorless MCQ

A particle is projected with a speed $2\sqrt{gh}$ so that it clears two walls of equal height h which are at a distance 2h from each other. The time taken by the particle to pass between the two walls is

A

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

B

$\frac{2h}{g}$

C

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

D

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

Question 41: Palette 41/118

Errorless MCQ

A projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal direction with a velocity of $147 \, ms^{-1}$ . Then the time after which its inclination with the horizontal is $45^{\circ}$ is

A

$15 \, s$

B

$10.98 \, s$

C

$5.49 \, s$

D

$2.745 \, s$

Question 42: Palette 42/118

Errorless MCQ

A cannon ball is fired with a velocity v in a direction making an angle $\theta$ with the horizontal. At the highest point of its path it breaks into two parts of equal masses. One of the parts retraces the initial path of the ball. The speed of the second part immediately after explosion in m/s will be

A

$\frac{3}{2}v\cos\theta$

B

$\sqrt{\frac{3}{2}}v\cos\theta$

C

$2v\cos\theta$

D

$3v\cos\theta$

Question 43: Palette 43/118

Errorless MCQ

From the top of a tower of height 40 m a ball is projected upwards with a speed of 20 m/s at an angle of elevation of $30^{\circ}$ . Then 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

4:1

Question 44: Palette 44/118

Errorless MCQ

A projectile fired with initial velocity u at some angle $\theta$ , has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be

A

2R

B

R/2

C

R

D

4R

Question 45: Palette 45/118

Errorless MCQ

The range of a particle when launched at an angle of $15^{\circ}$ with the horizontal is $1.5 \, km$ . What is the range of the projectile when launched at an angle of $45^{\circ}$ to the horizontal

A

$1.5 \, km$

B

$3.0 \, km$

C

$6.0 \, km$

D

$0.75 \, km$

Question 46: Palette 46/118

Errorless MCQ

Three identical balls are thrown with same speed at angles of $15^{\circ}$ , $45^{\circ}$ and $75^{\circ}$ with the horizontal respectively. The ratio of their distances from the point of projection to the where they hit the ground will be

A

$1:\sqrt{2}:1$

B

$1:2:1$

C

$2:4:3$

D

$1:2:\sqrt{3}$

Question 47: Palette 47/118

Errorless MCQ

Five balls A, B, C, D and E are projected with the same speed making angles of $10^{\circ}$ , $30^{\circ}$ , $45^{\circ}$ , $60^{\circ}$ , $80^{\circ}$ respectively with the horizontal. Which ball will strike the ground at the farthest point

A

B

B

A

C

E

D

C

Question 48: Palette 48/118

Errorless MCQ

An object is thrown along a direction inclined at an angle of $45^{\circ}$ with the horizontal direction. The horizontal range of the particle is equal to

A

Vertical height

B

Twice the vertical height

C

Thrice the vertical height

D

Four times the vertical height

Question 49: Palette 49/118

Errorless MCQ

A projectile is thrown at an angle of $40^{\circ}$ with the horizontal and its range is $R_{1}$ . Another projectile is thrown at an angle $40^{\circ}$ with the vertical and its range is $R_{2}$ . What is the relation between $R_{1}$ and $R_{2}$

A

$R_{1} = R_{2}$

B

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

C

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

D

$R_{1} = 4R_{2}/5$

Question 50: Palette 50/118

Errorless MCQ

It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation of $\frac{5\pi}{36}$ radians should strike a given target. In actual practice it was found that a hill just intervened in the trajectory. At what angle of elevation should the gun be fired to hit the target

A

$\frac{5\pi}{36}$ rad

B

$\frac{11\pi}{36}$ rad

C

$\frac{7\pi}{36}$ rad

D

$\frac{13\pi}{36}$ rad

Question 51: Palette 51/118

Errorless MCQ

Two particles are projected from the same point with the same speed at different angle $\theta_{1}$ and $\theta_{2}$ to the horizontal. They have the same horizontal range. Their times of flight are $t_1$ and $t_2$ respectively. Then

A

$\theta_{1} + \theta_{2} = 90^{\circ}$

B

$\frac{t_1}{t_2} = \frac{\tan\theta_1}{\tan\theta_2}$

C

$\frac{t_1}{t_2} = \tan\theta_2$

D

$\frac{t_1}{t_2} = \tan\theta_1$

Question 52: Palette 52/118

Errorless MCQ

A projectile thrown from a height of 10 m with velocity of $\sqrt{2}$ m/s, the projectile will fall, from the foot of projection, at distance ( $g = 10 \, m/s^{2}$ )

A

1 m

B

2 m

C

3 m

D

$\sqrt{2}$ m

Question 53: Palette 53/118

Errorless MCQ

On throwing a ball from the top of a vertical tower with a horizontal velocity of 20 m/s, it hits the earth at a distance of 50 m from the foot of the tower. If the ball is thrown with the same horizontal velocity from the top of another tower of height four times the height of first tower, the ball will hit the earth at a distance of

A

50 m

B

100 m

C

200 m

D

$50\sqrt{2}$ m

Question 54: Palette 54/118

Errorless MCQ

A shell is fired vertically upwards with a velocity $v_{1}$ from the deck of a ship travelling at a speed of $v_{2}$ . A person on the shore observes the motion of the shell as parabola whose 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

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

Question 55: Palette 55/118

Errorless MCQ

A boy standing on a long rail road car throws a ball straight upward. The car is moving on the horizontal road with an acceleration of $1m / s^2$ and the projection velocity in the vertical direction is $9.8m / s$ . How far behind the boy will the ball fall on the car

A

$1m$

B

$2m$

C

$4m$

D

$0.5m$

Question 56: Palette 56/118

Errorless MCQ

Two projectiles A and B thrown with velocities v and $\frac{v}{2}$ have the same range. If B is thrown at an angle of $15^{\circ}$ to the horizontal, A must have been thrown at an angle

A

$\sin^{-1}\left(\frac{1}{16}\right)$

B

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

C

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

D

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

Question 57: Palette 57/118

Errorless MCQ

A body is projected with a speed u in such a direction that the maximum height obtained is equal to its horizontal range. The horizontal range is

A

$\frac{8u^{2}}{17g}$

B

$\frac{5u^{2}}{17g}$

C

$\frac{6u^{2}}{13g}$

D

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

Question 58: Palette 58/118

Errorless MCQ

A body of mass m thrown horizontally with velocity v, from the top of tower of height h touches the level ground at a distance of 250 m from the foot of the tower. A body of mass 2m, thrown horizontally with a velocity v/2, from the top of tower of height 4 h will touch the level ground at a distance from the foot of tower

A

250 m

B

500 m

C

125 m

D

$250 \sqrt{2}$ m

Question 59: Palette 59/118

Errorless MCQ

A small block of mass 0.1 kg is pressed against a horizontal spring fixed at one end to compress the spring through 5.0 cm as shown in figure. The spring constant is 100 N/m. When released the block moves

A

Vertically below the edge on which the mass is resting

B

At a horizontal distance of $1m$ from free end of the spring

C

At a horizontal distance of $2m$ from free end of the spring

D

At a horizontal distance of $\sqrt{2} m$ from free end of the spring

Question 60: Palette 60/118

Errorless MCQ

Which of the following does not affect the maximum height attained by the projectile

A

Magnitude of initial velocity

B

Acceleration of the projectile

C

Angle of projection

D

Mass of the projectile

Question 61: Palette 61/118

Errorless MCQ

A cricketer hits a ball with a velocity 25 m/s at $60^{\circ}$ above the horizontal. How far above the ground it passes over a fielder 50 m from the bat (assume the ball is struck very close to the ground)

A

8.2 m

B

9.0 m

C

11.6 m

D

12.7 m

Question 62: Palette 62/118

Errorless MCQ

A person can throw a stone to a maximum distance of 100 m. the greatest height to which he can throw the stone is

A

100 m

B

75 m

C

50 m

D

25 m

Question 63: Palette 63/118

Errorless MCQ

Which of the following is largest, when the height attained by the projectile is the largest

A

Range

B

Time of flight

C

Angle of projectile with vertical

D

None of these

Question 64: Palette 64/118

Errorless MCQ

In broad jumping does it matter how high you jump? What factors determine the span of the jump

A

Yes, $u$ and $\theta$

B

No, $u$ and $\theta$

C

No, $h$ and $\theta$

D

None of these

Question 65: Palette 65/118

Errorless MCQ

From a point on the ground at a distance 2 metres from the foot of a vertical wall, a ball is thrown at an angle of $45^{\circ}$ which just clears the top of the wall and afterward strikes the ground at a distance $4m$ on the other side. The height of the wall is

A

$\frac{2}{3} m$

B

$\frac{3}{4} m$

C

$\frac{1}{3} m$

D

$\frac{4}{3} m$

Question 66: Palette 66/118

Errorless MCQ

A ball is thrown from the top of a tower with an initial velocity of 10 m/s at an angle of $30^{\circ}$ above the horizontal. It hits the ground at a distance of 17.3 m from the base of the tower. The height of the tower ( $g = 10 \, m/s^{2}$ ) will be

A

10 m

B

12 m

C

110 m

D

100 m

Question 67: Palette 67/118

Errorless MCQ

A ball is projected from the ground at a speed of 10 m/s making angle $30^{\circ}$ with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. Both the balls collide at the maximum height of the projectile. What was the initial height of the second ball

A

1.0 m

B

1.25 m

C

2.0 m

D

2.5 m

Question 68: Palette 68/118

Errorless MCQ

A hose shoots a stream of water at an angle of $60^{\circ}$ the horizontal with a velocity of $20 \, m/s$ . Water will strike a wall at a distance of $10 \, m$ at a height

A

$5.36 \, m$

B

$10.22 \, m$

C

$12.42 \, m$

D

$16.84 \, m$

Question 69: Palette 69/118

Errorless MCQ

A particle of mass m is thrown at an angle of $45^{\circ}$ with the horizontal with a momentum p. The magnitude of its momentum at the top of its parabolic path will be

A

p

B

2 p

C

$p/\sqrt{2}$

D

p/2

Question 70: Palette 70/118

Errorless MCQ

A bullet of mass m is fired from a point at an angle of $45^{\circ}$ with the horizontal with a velocity v. When it reaches the ground, the change in its vertical component of momentum is

A

Zero

B

$\frac{1}{2}mv$

C

$mv\sqrt{2}$

D

2 mv

Question 71: Palette 71/118

Errorless MCQ

A ball of mass m and kinetic energy E is thrown at an angle of $45^{\circ}$ with the horizontal. The momentum at the highest point of its path will be

A

$\sqrt{mE}$

B

$\sqrt{mE/2}$

C

$\sqrt{2mE}$

D

Zero

Question 72: Palette 72/118

Errorless MCQ

A particle having a mass of 0.5 kg is projected under gravity with a speed of 98 m/sec at an angle of $60^{\circ}$ . The magnitude of the change in momentum in N-sec of the particle after 10 seconds is

A

0.5

B

49

C

98

D

490

Question 73: Palette 73/118

Errorless MCQ

A projectile is fired at $30^{\circ}$ with momentum $p$ . neglecting friction the change in momentum on return to the ground will be

A

Zero

B

$30\%$

C

$60\%$

D

$100\%$

Question 74: Palette 74/118

Errorless MCQ

A ball is thrown up with a given angle to the horizontal. Then the total change of momentum by the instant it returns to the ground is equal to

A

Acceleration due to gravity × total time of flight

B

Weight of the ball × half the time of flight

C

Weight of the ball × total time of flight

D

None of these

Question 75: Palette 75/118

Errorless MCQ

The work done to project a body with a certain velocity is W. What extra work is required to be done to double its velocity

A

W

B

2W

C

3W

D

4W

Question 76: Palette 76/118

Errorless MCQ

A cricket ball is hit at $30^{\circ}$ with the horizontal with kinetic energy $K$ . The kinetic energy at the highest point is

A

Zero

B

$K / 4$

C

$K / 2$

D

$3K / 4$

Question 77: Palette 77/118

Errorless MCQ

Two balls are projected, one vertically up and the other at an angle of $30^{\circ}$ to the horizontal, with the same initial speed. The potential energy at the highest point will be in the ratio

A

$3:4$

B

$4:3$

C

$4:1$

D

$1:4$

Question 78: Palette 78/118

Errorless MCQ

In the above problem the ratio of kinetic energies of these balls at the highest point is

A

$4:3$

B

$3:4$

C

$\infty$

D

o

Question 79: Palette 79/118

Errorless MCQ

A body is projected such that the K.E. at the topmost position is half of the initial K.E. What is its angle of projection with the horizontal

A

$30^{\circ}$

B

$60^{\circ}$

C

$75^{\circ}$

D

$45^{\circ}$

Question 80: Palette 80/118

Errorless MCQ

A body is thrown with initial kinetic energy 100J at an angle $\theta^{\circ}$ to the horizontal. If its kinetic energy at the top is 25J, then the angle of projection is

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$90^{\circ}$

Question 81: Palette 81/118

Errorless MCQ

A particle moves along a circular path of radius $r$ with uniform speed $v$ . The angle described by the particle in one second is given by

A

$vr^{-1}$

B

$v^{-1}r$

C

$vr^{-2}$

D

$v^2 r$

Question 82: Palette 82/118

Errorless MCQ

The angular velocity of earth about its axis of rotation is

A

$2\pi/(60 \times 60 \times 24)$ rad/sec

B

$2\pi/(60 \times 60)$ rad/sec

C

$2\pi/60$ rad/sec

D

$2\pi/(365 \times 24 \times 60 \times 60)$ rad/sec

Question 83: Palette 83/118

Errorless MCQ

The ratio of the angular velocities of rotational motion of earth round the sun and spinning motion about its own axis is

A

1/12

B

1/24

C

1/365

D

1/3600

Question 84: Palette 84/118

Errorless MCQ

The ratio of an angular speed of hours hand and seconds hand of a clock is 210 Motion In Two Dimension

A

1 : 1

B

1 : 60

C

1 : 720

D

3600 : 1

Question 85: Palette 85/118

Errorless MCQ

A racing car is travelling along a track at a constant speed of 40 m/s. A T.V. camera men is recording the event from a distance of 30m directly away from the track as shown in figure. In order to keep the car under view in the position shown, the angular speed with which the camera sh

A

4/3 rad/sec

B

3/4 rad/sec

C

8/3 $\sqrt{3}$ rad/sec

D

1 rad/sec

Question 86: Palette 86/118

Errorless MCQ

A particle is moving along a circular path with angular speed $\omega$ about the axis passing through the centre. What will be its angular speed about a point on the other end of the diameter through the instantaneous position of the particle

A

$2\omega$

B

$\omega$

C

$\omega/2$

D

$\omega/4$

Question 87: Palette 87/118

Errorless MCQ

The linear velocity of a point on the equator is nearly (radius of the earth is 6400 km)

A

800 km/hr

B

1600 km/hr

C

3200 km/hr

D

6400 km/hr

Question 88: Palette 88/118

Errorless MCQ

The second's hand of a watch has length 6 cm. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

A

6.28 and 0 mm/s

B

8.88 and 4.44 mm/s

C

8.88 and 6.28 mm/s

D

6.28 and 8.88 mm/s

Question 89: Palette 89/118

Errorless MCQ

An aeroplane is moving in a horizontal circle with a uniform speed of 141 km/hr. Change in its velocity in one fourth revolution, from its initial direction will be

A

100 km/hr at an angle of $90^{\circ}$

B

141 km/hr at an angle of $135^{\circ}$

C

200 km/hr at an angle of $135^{\circ}$

D

Zero

Question 90: Palette 90/118

Errorless MCQ

The linear and angular acceleration of a particle are $10 \, m/sec^{2}$ and $5 \, rad/sec^{2}$ respectively it will be at a distance from the axis of rotation

A

50 m

B

$1/2 \, m$

C

1 m

D

2 m

Question 91: Palette 91/118

Errorless MCQ

On applying brakes the angular velocity of a flywheel reduces from 900 cycles/min to 720 cycles/min in 6 seconds. Its angular retardation in $rad/s^2$ will be

A

$\pi/3$

B

$\pi$

C

$2\pi/3$

D

$2\pi$

Question 92: Palette 92/118

Errorless MCQ

A particle is moving in a circular path with velocity varying with time as $v = 1.5 t^{2} + 2t$ . If 2cm the radius of circular path, the angular acceleration at t = 2 sec will be

A

$4 rad/sec^{2}$

B

$40 rad/sec^{2}$

C

$400 rad/sec^{2}$

D

$0.4 rad/sec^{2}$

Question 93: Palette 93/118

Errorless MCQ

A stone, tied at the end of a string 80 cm long, is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of acceleration of the stone

A

$680 \, cm/s^{2}$

B

$720 \, cm/s^{2}$

C

$860 \, cm/s^{2}$

D

$990 \, cm/s^{2}$

Question 94: Palette 94/118

Errorless MCQ

What happens to the centripetal acceleration of a revolving body if you double the orbital speed v and half the angular velocity $\omega$

A

The centripetal acceleration remains unchanged

B

The centripetal acceleration is halved

C

The centripetal acceleration is doubled

D

The centripetal acceleration is quadrupled

Question 95: Palette 95/118

Errorless MCQ

The mean distance of the moon from the earth is $3.84 \times 10^{8} m$ . The moon makes one revolution round the earth in $2.34 \times 10^{6}$ sec. The acceleration of the moon towards the earth is

A

$2.73 \times 10^{-3} m/s^{2}$

B

$2.73 \times 10^{-2} m/s^{2}$

C

$0.273 m/s^{2}$

D

$2.73 \times 10^{-4} m/s^{2}$

Question 96: Palette 96/118

Errorless MCQ

An astronaut is rotating in a rotor of radius $4m$ . If he can withstand maximum acceleration of $10g$ , the maximum permissible frequency of rotor will be

A

$\frac{\pi}{5} Hz$

B

$\frac{2\pi}{5} Hz$

C

$\frac{5\pi}{5} Hz$

D

$\frac{5}{2\pi} Hz$

Question 97: Palette 97/118

Errorless MCQ

Two masses M and m are attached to a vertical axis by weightless threads of combined length L. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega$ . If the tensions in the threads are the same during motion, the distance of M from the axis is

A

$\frac{Ml}{M+m}$

B

$\frac{ml}{M+m}$

C

$\frac{M+m}{M}l$

D

$\frac{M+m}{m}l$

Question 98: Palette 98/118

Errorless MCQ

In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If $a_0$ is the radius of the ground state orbit, $m$ is the mass, $e$ is the charge on the electron and $\varepsilon_0$ is the vacuum permittivity, then speed of the electron is

A

$\sqrt{\frac{\varepsilon_0a_0m}{e}}$

B

$\frac{e}{\sqrt{\varepsilon_0a_0m}}$

C

$\frac{\sqrt{4\pi\varepsilon_0a_0m}}{e}$

D

$\frac{e}{\sqrt{4\pi\varepsilon_0a_0m}}$

Question 99: Palette 99/118

Errorless MCQ

A rubber band of length l has a stone of mass m tied to its one end. It is whirled with speed v so that the stone describes a horizontal circular path. The tension T in the rubber band is

A

Zero

B

$mv^{2}/l$

C

$>(mv^{2})/l$

D

$

Question 100: Palette 100/118

Errorless MCQ

A particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum. The radial force acting on the particle is

A

pmr

B

$\frac{rm}{p}$

C

$\frac{mp^{2}}{r}$

D

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

Question 101: Palette 101/118

Errorless MCQ

Two particles of equal masses are revolving in circular paths of radii $r_1$ and $r_2$ respectively with the same speed. The ratio of their centripetal forces is

A

$\frac{r_2}{r_1}$

B

$\sqrt{\frac{r_2}{r_1}}$

C

$\left(\frac{r_1}{r_2}\right)^2$

D

$\left(\frac{r_2}{r_1}\right)^2$

Question 102: Palette 102/118

Errorless MCQ

A particle of mass m is observed from an inertial frame of reference and is forced to move in a circle of radius r with a uniform speed v. The centrifugal force on it is

A

$\frac{mv^{2}}{r}$ towards the centre

B

$\frac{mv^{2}}{r}$ away from the centre

C

$\frac{mv^{2}}{r}$ along the tangent through the particle

D

Zero

Question 103: Palette 103/118

Errorless MCQ

A bowl, containing water and mercury, is revolved rapidly about a vertical axis, then the liquid which remains outermost is

A

Water

B

Mercury

C

Mercury and water both

D

None of the above

Question 104: Palette 104/118

Errorless MCQ

The tube AB forms a quarter circle in a vertical plane. The particle Pcan move without friction in the tube. P is placed at A and displaced slightly. It will

A

Always be in contact with the outer wall

B

Always be in contact with the inner wall

C

Initially be in contact with the inner wall and later with the outer wall

D

Initially be in contact with the outer wall and later with the inner wall

Question 105: Palette 105/118

Errorless MCQ

A small block of mass 0.1kg moves with uniform speed in a horizontal circular groove of radius 1m. The block takes $\pi$ sec to complete one round. The normal contact force by the side will be

A

0.25 N

B

0.4 N

C

0.56 N

D

0.1 N

Question 106: Palette 106/118

Errorless MCQ

A particle of mass $m_{1}$ is fastened to one end of a string and one of $m_{2}$ to the middle point, the other end of the string being fastened to a fixed point on a smooth horizontal table. The particles are then projected, so that the two portions of the string are always in the same straight line and describes horizontal circles. Find the ratio of tensions in the two parts of the string

A

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

B

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

C

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

D

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

Question 107: Palette 107/118

Errorless MCQ

A toy cart is tied to the end of an unstretched string of length $a$ . When revolved, thy toy cart moves in a horizontal circle of radius $2a$ with a time period $T$ . Now the toy cart is speeded up until it moves in a horizontal circle of radius $3a$ with a period $T'$ . If Hooke's law holds, then

A

$T' = T$

B

$T' = (3/2)T$

C

$T' = (\sqrt{3}/2)T$

D

$T' = \sqrt{(3/2)}T$

Question 108: Palette 108/118

Errorless MCQ

A chain of 125 links is $1.25m$ long and has a mass of $2kg$ . With the ends fastened together it is set rotating at $3000 \text{ rev/min}$ . Find the centripetal force on each link

A

$3.14N$

B

$314 N$

C

$\frac{1}{3.14} N$

D

$\frac{1}{314} N$

Question 109: Palette 109/118

Errorless MCQ

Two bodies $A$ and $B$ each of mass $m$ are tied together by a light string. Both bodies are bound to move on a frictionless ring in a vertical plane as shown in figure. Both bodies are released from rest from the positions shown in figure. Just after releasing, the tension in the string will be

A

2mg

B

$\frac{mg}{2}$

C

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

D

$mg\sqrt{2}$

Question 110: Palette 110/118

Errorless MCQ

A cylindrical tube of length ‘l’ radius ‘r’ is filled by liquid of density p is rotated ( $\omega$ ), horizontally about an axis-through one of its edges. The force at the other end by the liquid is,

A

$\rho\pi r^{2}\omega^{2}l^{2}$

B

$\frac{\rho\pi r^{2}\omega^{2}l}{2}$

C

$\frac{\rho\pi r^{2}\omega^{2}l^{2}}{2}$

D

None of these

Question 111: Palette 111/118

Errorless MCQ

A car moves along a horizontal circular road of radius $r$ with velocity $v$ . The coefficient of friction between the wheels and the road is $\mu$ . Which of the following statements is not true

A

The car will slip if $v > \sqrt{\mu rg}$

B

The car will slip if $\mu < \frac{v^2}{rg}$

C

The car will slip if $r > \frac{v^2}{\mu g}$

D

The car will slip at a lower speed, along with some acceleration, than if it moves at constant speed

Question 112: Palette 112/118

Errorless MCQ

A cyclist riding the bicycle at a speed of $14\sqrt{3}ms^{-1}$ takes a turn around a circular road of radius $20\sqrt{3}m$ without skidding. (Given $g = 9.8ms^{-2}$ ), what is his inclination to the vertical

A

$30^{\circ}$

B

$90^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 113: Palette 113/118

Errorless MCQ

A racing car of 1000 kg moves round a banked track at a constant speed of 108 km/hr. Assuming the total reaction at the wheels is normal to the track and the horizontal radius of the track is 100m, calculate the angle of inclination of the track to the horizontal (take $g = 10 \, m/s^{2}$ )

A

$12^{o}$

B

$27^{o}$

C

$42^{o}$

D

$65^{o}$

Question 114: Palette 114/118

Errorless MCQ

In the above question, what is the reaction at the wheels

A

$13450N$

B

$26900N$

C

$6725N$

D

$40350N$

Question 115: Palette 115/118

Errorless MCQ

A car is moving with a speed v on a road inclined at an angle $\theta$ in a circular arc of radius r, the minimum coefficient of friction, so that the car does not slip away

A

$\frac{v^{2}}{rg} = \mu \tan \theta$

B

$\mu = v^{2} / rg$

C

$\frac{v^{2} \cos \theta - rg \sin \theta}{rg \cos \theta + v^{2} \sin \theta}$

D

$\frac{v^{2} \cos \theta - rg \sin \theta}{rg \cos \theta - v^{2} \sin \theta}$

Question 116: Palette 116/118

Errorless MCQ

A 2kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4m/sec. The tension in the string will be 52 N, when the stone is

A

At the top of the circle

B

At the bottom of the circle

C

Halfway down

D

None of the above

Question 117: Palette 117/118

Errorless MCQ

A particle of mass M carries a charge +Q. It is attached to a string of length l and is whirled in a vertical circle in electric field $\vec{E}$ directed upwards; what should be the minimum speed of the path the loop

A

$[(g + QE / M)l]^{1/2}$

B

$[(g - QE / M)l]^{1/2}$

C

$[(Mg + QE)l]^{1/2}$

D

$[(Mg - QE)l]^{1/2}$

Question 118: Palette 118/118

Errorless MCQ

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A

$\sqrt{u^{2}-2gL}$

B

$\sqrt{2gL}$

C

$\sqrt{u^{2}-gl}$

D

$\sqrt{2(u^{2}-gL)}$