COE in Elastic Collision

Q.

If two identical shapes undergo elastic collision, then the velocities of the object gets ……. after collision.

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

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 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 $\frac{v}{2}$

2. Both P and Q move forward with speed $\frac{v}{\sqrt{2}}$

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

4. P and Q move in opposite directions with speed $\frac{v}{\sqrt{2}}$

Q. Initially, the spring is at its natural length and collision between blocks of mass $m\&m$ is elastic. The horizontal surface is smooth. Then, maximum compression of the spring during the motion will be:

1. $\sqrt{\frac{m{v}^2}{k}}$
2. $\sqrt{\frac{m{v}^2}{3k}}$
3. $\sqrt{\frac{2m{v}^2}{k}}$
4. $\sqrt{\frac{2m{v}^2}{3k}}$

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 the loss in the kinetic energy of the system due to collision.

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

Q. Two balls of masses $m_1\text{and}{m}_2$ ($m_2>>m_1$) 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. $v_1+v_2$
2. $v_1$
3. $v_2$
4. Data insufficient

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 the loss in the kinetic energy of the system due to collision.

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

Q. In the given figure, all the collisions are elastic. Find the velocity of $n^{th}$ ball after collision.

1. $2^{n-1}u$
2. $3^{n-1}u$
3. ${\left(\frac{2}{3}\right)}^{n-1}u$
4. ${\left(\frac{3}{2}\right)}^{n-1}u$

Q. Two masses each of mass $0.10\text{kg}$ are moving with velocity $3\text{m/s}$ along $x$ axis and $5\text{m/s}$ along $y$ axis respectively. After an elastic collision, one of the masses moves with a velocity $4\hat{i}+4\hat{j}$. The energy of the other mass after collision is

1. $0\text{J}$
2. $1\text{J}$
3. $0.1\text{J}$
4. $1.4\text{J}$

Q. Two metal balls of masses $10\text{kg}$ and $20\text{kg}$, moving in opposite directions on a frictionless floor, collide elastically. If the velocities of the balls are $3\text{m/s}$ and $1\text{m/s}$ respectively before collision as shown in the figure, then the velocities of the balls after collision are respectively

1. $\frac{5}{3}\text{m/s}$ towards left, $\frac{7}{3}\text{m/s}$ towards right
2. $\frac{5}{3}\text{m/s}$ towards left, $\frac{7}{3}\text{m/s}$ towards left
3. $\frac{5}{3}\text{m/s}$ towards right, $\frac{7}{3}\text{m/s}$ towards right
4. $\frac{7}{3}\text{m/s}$ towards left, $\frac{5}{3}\text{m/s}$ towards right

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.

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. $\pi \text{s}$