COE in Elastic Collision

Q.

A particle of mass $100g$ moving at an initial speed $u$ collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes $0.2J$ after the collision, what could be the minimum and the maximum value of $u$?

1. m/s, m/s

2. m/s, m/s

3. m/s, m/s

4. m/s, m/s

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.

In an elastic collision in one dimension if a body A collides against the body B of equal mass at rest, then the body A will

1. moves with the same velocity in the same direction.

2. come to rest.

3. move with twice its initial velocity

4. moves with the same velocity but in opposite direction.

Q. Two perfectly elastic balls of the same mass $m$ are moving with velocities $u_1$ and $u_2$. They collide head on elastically, $n$ times. The kinetic energy of the sytem finally is

1. $\frac{1}{2}\frac{m}{n}{u}_1^2$
2. $\frac{1}{2}\frac{m}{n}(u_1^2+u_2^2)$
3. $\frac{1}{2}m(u_1^2+u_2^2)$
4. $\frac{1}{2}mn(u_1^2+u_2^2)$

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. 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.

A shell is fired vertically up. At some point it explodes in three parts with mass ratio 1:1:2 . One part falls at 10m left of projected point. Heavier part falls at 20 m right. What is the position of the third part?

1. 30 m left

2. 20 m left

3. 10 m left

4. 15 m left

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. 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. 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. Three blocks are initially placed seperately on a frictionless surface. Block A has mass m and initial velocity v to the right.Block B with mass m and block C with mass 4m are both initially at rest. All collisions are elastic. The final velocity of block A is ?

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

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. $\pi \text{s}$