COE in Elastic Collision

Q.

A particle P moving with speed 'v' undergoes a head-on elastic collision with another particle Q of identical mass and at rest. After the collision,

1. Both P and Q move forward with speed

2. Both P and Q move forward with speed

3. P comes to rest and Q moves forward with speed v

4. P and Q move in opposite directions with speed

Q.

A perfectly elastic ball $P_1$ of mass m moving with velocity v collides elastically with three exactly similar balls $P_2,P_3,P_4$ lying on a smooth table as shown. Velocities of the four balls after the collision are

1. v, v, v, v

2. 0, 2v, 3v, 4v

3. 0, 0, 0, v

4. 0, 0, 0, 0

Q. A ball of mass 'm' moving horizontally at a speed 'v' collides with the bob of a simple pendulum at rest. The mass of the bob is also' 'm, if the collision is perfectly elastic, the bob of the pendulum will rise to a height of

1. 
2. 
3. 
4. 

Q. Body $A$ of mass $4m$moving with speed $u$ collides with another body $B$ of mass $2m$ at rest. The collision is head on and elastic in nature. After the collision, the fraction of kinetic energy lost by the colliding body $A$ is

1. $\frac{1}{9}$
2. $\frac{8}{9}$
3. $\frac{4}{9}$
4. $\frac{5}{9}$

Q. In collision, total energy is conserved only

1. if it is perfectly elastic.
2. if it is perfectly inelastic.
3. if it is either perfectly elastic or perfectly inelastic.
4. None of these.

Q. A particle of mass $100\text{g}$ moving with a speed $1\text{m/s}$ collides perfectly inelasticaly with another particle of mass $200\text{g}$ initially at rest. Find loss in kinetic energy of the system during collision.

1. 0.066 J
2. 0.033 J
3. 0.33 J
4. 3.33 J

Q.

Two balls $a$ and $b$ of same mass are moving on a circular path of radius $r=1\text{m}$ with constant velocity of $5\text{m/s}$ and $15\text{m/s}$ as shown in figure. If after some time both ball collides perfectly elastically, find the time $t$ when they will collide again. Friction is absent everywhere.

1. $\frac{\pi }{5}\text{s}$
2. $\frac{2\pi }{5}\text{s}$
3. $\frac{\pi }{10}\text{s}$
4. $\pi \text{s}$

Q. In the figure shown below, two particles have masses $2\text{kg}$ each and they are moving with velocities $4\text{m/s}$ and $2\text{m/s}$ respectively towards each other. Assume the collision between the particles is perfectly elastic. Find their respective magnitudes of velocities after the collision.

1. $v_1=3\text{m/s};v_2=3\text{m/s}$
2. $v_1=2\text{m/s};v_2=4\text{m/s}$
3. $v_1=4\text{m/s};v_2=4\text{m/s}$
4. $v_1=2\text{m/s};v_2=3\text{m/s}$

Q. A particle of mass ${}^{\prime }{m}^{\prime }$ is moving with speed $8\text{m/s}$ on a frictionless surface as shown in figure. If $m<<M$, then for one dimensional elastic collision, the speed of the lighter particle after collision will be

1. $4\text{m/s}$ in original direction
2. $6\text{m/s}$ in original direction
3. $4\text{m/s}$ opposite to the original direction
4. $6\text{m/s}$ opposite to the original direction.

Q. Two balls of masses $m_1\text{and}{m}_2$ such that ($m_2>>m_1$) are moving with initial velocities $v_1\text{and}{v}_2$ respectively towards each other. The final velocity of $m_2$ after collision will be [Assume collision to be perfectly elastic]

1. Data insufficient
2. $v_1+v_2$
3. $v_1$
4. $v_2$