Bouncing Ball Example

Q. A ball of mass 5kg moving with speed 8m/s collides head on with another stationary ball of mass 15kg if collision is perfectly in elastic then loss in kinetic energy is 1) 160J 2 )80J 3) 40J 4 )120J

Q. A ball of mass 3M rolls from rest on a smoothflat table towards another ball of mass 2M atrest with a constant velocity 5m/s. When thetwo balls are separated by a distance 6m, theposition of centre of mass from the mass 3M is

Q. A bullet of mass m moving with velocity u strikes a block of mass M at rest and gets embedded in the block the loss of kinetic energy in the impact is

Q.

A ball of mass $m$ moving with a speed $u$ collides elastically with another identical ball moving with velocity $u_2$. Find the angle between velocities after collision if they collide obliquely and $u_2$ = 0​

1. 

2. 

3. 

4. zero

Q. a body of mass M moving with velocity V collides head on elastic collision with another identical body at rest. the percentage loss in kinetic energy of the first body will be

Q. A neutron mass $1.67\times {10}^{-27}kg$ moving with a velocity $1.2\times {10}^{7}m{s}^{-1}$ collides head-on with a deuteron of mass $3.34\times {10}^{-27}kg$ initially at rest. If the collision is perfectly inelastic, the speed of the composite particle will be

1. 
2. 
3. 
4. 

Q.

A ball drops from the ceiling of the room, and after rebounding twice from the floor, reaches a height equal to half that of ceiling. Find the coefficient of restitution?

1. 

2. 

3. 

4. 

Q.

A particle is thrown up with velocity $v_0$ inside a stationary lift of sufficient height. The time of flight is 'T'. Now it is thrown again with same initial speed $v_0$ with respect to lift. If at the time of second thrown, lift is moving up with a velocity $v_0$ and uniform acceleration g upward. Which of the following are true?

1. (a)Displacement-time graph of particle when lift was stationary

   

2. (b)Displacement-time graph of the particle with respect to the moving lift.

   

3. (c)Displacement-time graph of the particle with respect to ground when the lift is moving

   

4. (d) Velocity-time graph of the particle with respect to the moving lift.

   

Q. A body of mass 1 kg moving with speed 2m/s collides elastically with another body of mass 1.5kg initially at rest .The fractional kinetic energy retained by the lighter body.

Q. 17. Two wires Ac and Bc are tied at c of small sphere of mass 5 kg which revolves at a constant speed v in the horizontal circle of radius 1.6m the minimum value of v is (a) 3.01 m/s (b)4.01 m/s (C) 8.2 m/s (d) 3.96 m/s

Q. A ball is projected with an initial speed $u$ at an angle $\theta$ from the horizontal ground. The coefficient of restitution between the ball and the ground is $e$. Find the position from the starting point when the ball will land on the ground for the $2^{nd}$ time.

1. $\frac{e^2{u}^2\sin 2\theta }{g}$
2. $\frac{(1-e^2)u^2\sin 2\theta }{g}$
3. $\frac{(1-e)u^2\sin \theta \cos \theta }{g}$
4. $\frac{(1+e)u^2\sin 2\theta }{g}$

Q.

A steel ball falls from a height ‘h’ on a floor for which the coefficient of restitution is e. The height attained by the ball after the first rebounds is

1. $he$
2. $h{e}^2$
3. $h/e$
4. $h/e^2$

Q. A ball is thrown upwards from the bottom of a fixed chamber of height $20\text{m}$ with a speed of $10\text{m/s}$. The interior of the chamber has no gravity. The ball strikes the ceiling of the chamber and rebounds. After $6\text{seconds}$, gravity is reintroduced in the chamber. The movement of the ball gradually slows down over time and the ball comes to rest. Which of the following is the correct displacement vs time graph for the movement of the ball inside the chamber?

1. 
2. 
3. 
4. 

Q. A ball is projected in a direction inclined to the horizontal and it bounces on a horizontal plane. If the range of first rebound is $R$ and coefficient of restitution is $e$, then range of the next rebound is

1. $R^{\prime }=eR$
2. $R^{\prime }=e^{2}R$
3. $R^{\prime }=\frac{R}{e}$
4. $R^{\prime }=R$

Q. A ball is projected from a point in one of the two smooth parallel vertical walls against the other in a plane perpendicular to both. After being reflected at each wall impinge again on the second at a point in the same plane as it started. The distance between two walls is $a.b$ is the free range and $e$ be the coefficient of restitution:

1. The total time taken in moving from $O$ to $C$ is $\frac{a}{e^{2}u}(e^2+e+1)$
2. The free range on the horizontal plane $b=\frac{2uv}{g}$
3. $b{e}^2=a(e^2+e+1)$
4. All of these

Q. A ball of mass 5kg moving with speed 8m/s collides head on with another stationary ball of mass 15kg if collision is perfectly in elastic then loss in kinetic energy is 1) 160J 2 )80J 3) 40J 4 )120J

Q. A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total time taken by the body to come to rest is

1. $\sqrt{\frac{2h}{g}}$
2. $2\sqrt{\frac{2h}{g}}$
3. $3\sqrt{\frac{2h}{g}}$
4. $4\sqrt{\frac{2h}{g}}$