Perfectly Elastic Collision

Q.

In head on elastic collision of two bodies of equal masses

1. The velocities are interchanged

2. The speeds are interchanged

3. The momenta are interchanged

4. The faster body slows down and the slower body speeds up

Q. For a perfectly inelastic collision, the value of coefficient of restitution is

1. equal to 0
2. less than 1
3. equal to 1
4. less than or equal to 1

Q.

As shown in figure, the block B of mass m starts from the rest at the top of a wedge W of mass M. All surfaces are without friction. W can slide on the ground, B slides down onto the ground, moves along it with a speed v, has an elastic collision with wall, and climbs back onto W. Then:

1. $B$ will reach the top of $W$ again

2. From the beginning, till the collision with the wall, the center of mass of ${}^{\prime }B$ plus $W^{\prime }$ is stationary

3. After the collision, the center of mass of ${}^{\prime }B$ plus $W^{\prime }$ moves with a velocity $\frac{2mv}{m+M}$

4. When $B$ reaches its highest position on $W$, the speed of $W$ is $\frac{2mv}{m+M}$

Q.

In an elastic collision of two particles the following is conserved

1. Momentum of each particle

2. Speed of each particle

3. Kinetic energy of each particle

4. Total kinetic energy of both the particles

Q. Two identical billiard balls are in contact on a smooth table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is

1. $\frac{2}{3}$
2. $\frac{1}{3}$
3. $\frac{1}{6}$
4. $\frac{\sqrt{3}}{2}$

Q. In a head on elastic collision of a heavy vehicle moving with a velocity of $10{\text{ms}}^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to

1. $5{\text{ms}}^{-1}$
2. $10{\text{ms}}^{-1}$
3. $20{\text{ms}}^{-1}$
4. $40{\text{ms}}^{-1}$

Q.

A ball $A$ is falling vertically downwards with velocity $v_1$. It strikes elastically with a wedge moving horizontally with velocity $v_2$ as shown in figure. What must be the ratio so that the ball bounces back in vertically upwards direction relative to wedge?

1. $\sqrt{3}$

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

3. 2

4. $\frac{1}{2}$

Q. Two identical balls A and B having velocities of $0.5m/s$ and $–0.3m/s$ respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be

1. $–0.3m/s$ and $0.5m/s$
2. $0.3m/s$ and $0.5m/s$
3. $-0.5m/s$ and $0.3m/s$
4. $0.5m/s$ and $-0.3m/s$

Q. A small steel ball $A$ is suspended by an inextensible thread of length $l=1.5\text{m}$ from $O$ as shown in the figure. Another identical ball $B$ is thrown vertically downwards such that its surface remains just in contact with thread during downward motion and collides elastically with the suspended ball. If the suspended ball just complete vertical circle after collision, calculate the Impulse on the steel ball $A$ due to the ball $B$. (Take $g=10{\text{m/s}}^2$ and mass of ball $m=5\text{kg}$)

1. $50\sqrt{2}\text{Ns}$
2. $25\sqrt{3}\text{Ns}$
3. $50\sqrt{3}\text{Ns}$
4. $25\text{Ns}$

Q. A ball of mass $m$ moving with a velocity $v$ hits a massive wall of mass $M(M>>m)$ moving towards the ball with a velocity $u$. An elastic impact lasts for a time $\Delta t$.

1. The average elastic force acting on the ball is $\frac{m(u+v)}{\Delta t}$
2. The average elastic force acting on the ball is $\frac{2m(u+v)}{\Delta t}$
3. The kinetic energy of the ball increases by $2mu(u+v)$
   
4. The kinetic energy of the ball remans the same after the collision.

Q.

Two perfectly elastic particles P and Q of equal mass travelling along the line joining them with velocities 15 m/sec and 10 m/sec. After collision, their velocities respectively (in m/sec) will be

1. 0, 25

2. 5, 20

3. 10, 15

4. 20, 5

Q. A ball falls on an inclined plane of inclination $\theta ={30}^{\circ }$ from a height $h=10\text{m}$ above the point of impact and makes a perfectly elastic collision. Find the distance where will it hit the plane again from the initial point of impact. $(\text{Take}g=10{\text{m/s}}^2)$

1. $20\text{m}$
2. $40\text{m}$
3. $10\text{m}$
4. $80\text{m}$

Q.

Two blocks $A$ and $B$ having the same mass collide elastically with each other. the velocity of block $A$ before the collision is $10\text{m/s}$. If block $A$ comes to rest after collision, then what was the velocity of block $B$ before the collision?

1. $10\text{m/s}$
2. $0\text{m/s}$
3. $20\text{m/s}$
4. $30\text{m/s}$

Q.

A smooth sphere of mass 'M' moving with velocity 'u' directly collides elastically with another sphere of mass 'm' at rest. After collision their final velocities are 'V' and 'v' respectively. The value of 'v' is

1. $\frac{2uM}{m}$

2. $\frac{2um}{M}$

3. $\frac{2u}{1+\frac{m}{M}}$

4. $\frac{2u}{1+\frac{M}{m}}$

Q.

Example: The bob $A$ of a pendulum released from ${30}^{\circ }$ to the vertical hits another bob $B$ of the same mass at rest on table as shown in figure. How high does the bob $A$ rise after the collision? Neglect the size of the bob and assume the collision to be elastic.

1. $L-\frac{L\sqrt{3}}{2}$

2. $L-\frac{L}{2}$

3. zero

4. $L-L\sqrt{\frac{2}{3}}$

Q. A simple pendulum is made of a string of length $l$ and a bob of mass $m$, is released from a small angle ${\theta }_0$. It strikes a block of mass $M$, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle ${\theta }_1$. Then, $M$ is given by

1. $m\left(\frac{{\theta }_0+{\theta }_1}{{\theta }_0-{\theta }_1}\right)$
2. $\frac{m}{2}\left(\frac{{\theta }_0-{\theta }_1}{{\theta }_0+{\theta }_1}\right)$
3. $m\left(\frac{{\theta }_0-{\theta }_1}{{\theta }_0+{\theta }_1}\right)$
4. $\frac{m}{2}\left(\frac{{\theta }_0+{\theta }_1}{{\theta }_0-{\theta }_1}\right)$

Q.

The bob A of a pendulum released from a height h hits head-on another bob B of the same mass of an identical pendulum initially at rest. What is the result of this collision? Assume the collision to be elastic.

1. Bob A comes to rest at B and bob B moves to the left attaining a maximum height h.

2. Bobs A and B both move to the left, each attaining a maximum height $\frac{h}{2}$.

3. Bob B moves to the left and bob A moves to the right, each attaining a maximum height $\frac{h}{2}$.

4. Both bobs come to rest.

Q.

$n$ small balls, each of mass $m$, impinge elastically each second on a surface with velocity $u$. The force experienced by the surface will be

1. $mnu$

2. $2mnu$

3. $4mnu$

4. $\frac{1}{2}mnu$

Q. A mass of $1\text{kg}$ collides elastically with a stationary mass of $5\text{kg}$. After collision, the $1\text{kg}$ mass reverses its direction and moves with a speed of $2\text{m/s}$. Which of the following statement(s) is/are correct ?

1. Total momentum of the system is $3\text{kg m/s}$
2. Momentum of $5\text{kg}$ mass after collision is $4\text{kg m/s}$
3. Kinetic energy of the centre of mass of system is $0.75\text{J}$
4. Kinetic energy of the centre of mass of system is $1.75\text{J}$

Q.

A particle of mass 'm' is moving with horizontal speed 6 m/sec as shown in figure. If m << M, then for one dimensional elastic collision, the speed of lighter particle after collision will be

1. 2m/sec in original direction

2. 2 m/sec opposite to the original direction

3. 4 m/sec opposite to the original direction

4. 4 m/sec in original direction

Q.

A heavy steel ball of mass greater than 1 kg moving with a speed of 2 $mse{c}^{-1}$collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed

1. $2mse{c}^{-1}$

2. $4mse{c}^{-1}$

3. $2\times {10}^{4}mse{c}^{-1}$

4. $2\times {10}^{3}mse{c}^{-1}$

Q. A ball of mass $m$ strikes the fixed inclined plane after falling through a height $h$. If it rebounds elastically, the impulse imparted on the ball is

1. $2m\sqrt{2gh}\cos \theta$
2. $2m\sqrt{gh}\cos \theta$
3. $2m\sqrt{2gh}\sin \theta$
4. $2m\sqrt{2gh}$

Q. Two balls having masses $m_1=5\text{kg}$ and $m_2=10\text{kg}$ moving with velocities $u_1=10\text{m/s}$ and $u_2=5\text{m/s}$ collide elastically. Find the change in momentum of the ball having mass $m_1$ due to collision

1. $110\text{kgm/s}$
2. $90\text{kgm/s}$
3. $-100\text{kgm/s}$
4. $50\text{kgm/s}$

Q. A moving particle of mass 'm' makes a head-on collision with a particle of mass '2m' initially at rest. If the collision is perfectly elastic, the percentage loss of energy of the colliding particle is

1. $50\%$
2. $66.7\%$
3. $88.9\%$
4. $100\%$

Q. A particle of mass $m$ moving with velocity $1\text{m/s}$ collides elastically with another particle of mass $2m$ (initialy at rest). If the incident particle is deflected by ${90}^{\circ }$. The angle $\theta$ made by the heavier mass with the initial direction of motion of mass $m$ will be equal to:
(consider collision to be perfectly elastic)

1. ${60}^{\circ }$
2. ${45}^{\circ }$
3. ${15}^{\circ }$
4. ${30}^{\circ }$

Q. Ball $A$ having initial velocity $u=5\text{m/s}$ collides elastically with block $B$ initially at rest as shown in the figure. If both balls have the same mass, and the height of the tower is $h=20\text{m}$, find the horizontal distance $d$ traveled by ball $B$ before hitting the ground.

1. $10\text{m}$
2. $9\text{m}$
3. $11\text{m}$
4. $12\text{m}$

Q. Two identical balls A and B having velocities of $0.5m/s$ and $–0.3m/s$ respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be

1. $–0.3m/s$ and $0.5m/s$
2. $0.3m/s$ and $0.5m/s$
3. $-0.5m/s$ and $0.3m/s$
4. $0.5m/s$ and $-0.3m/s$

Q. A wedge of mass $M$ has one face making an angle $\alpha$ with horizontal and is resting on a smooth rigid floor. A particle of mass ${}^{\prime }{m}^{\prime }$ hits the inclined face of the wedge with horizontal velocity $v_0.$ It is observed that the particle rebounds in vertical direction after impact. Calculate the speed of particle after impact.
[Neglect friction between particle and the wedge and take $M=2m,v_0=10\text{m/s},\tan \alpha =2,g=10{\text{m/s}}^2.$]

1. $5\text{m/s}$
2. $0\text{m/s}$
3. $20\text{m/s}$
4. $10\text{m/s}$

Q. A simple pendulum is made of a string of length $l$ and a bob of mass $m$, is released from a small angle ${\theta }_0$. It strikes a block of mass $M$, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle ${\theta }_1$. Then, $M$ is given by

1. $m\left(\frac{{\theta }_0+{\theta }_1}{{\theta }_0-{\theta }_1}\right)$
2. $\frac{m}{2}\left(\frac{{\theta }_0-{\theta }_1}{{\theta }_0+{\theta }_1}\right)$
3. $m\left(\frac{{\theta }_0-{\theta }_1}{{\theta }_0+{\theta }_1}\right)$
4. $\frac{m}{2}\left(\frac{{\theta }_0+{\theta }_1}{{\theta }_0-{\theta }_1}\right)$

Q. Two balls $A$ and $B$ having equal masses and moving along the same straight line with velocities $+2\text{m/s}$ and $-5\text{m/s}$ respectively, collide elastically. If rightwards direction is considered as $+vex-$ axis, then their velocities after the collision will be respectively

1. $-5\text{m/s}$ and $+2\text{m/s}$
2. $3\text{m/s}$ for both
3. $5\text{m/s}$ and $1\text{m/s}$
4. None of these