COE in Elastic Collision

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

Q.

Two bodies of masses $\mathrm{m}$ and $4\mathrm{m}$ are moving with equal linear momenta. The ratio of their kinetic energies is

1. $1:4$

2. $4:1$

3. $2:1$

4. $1:2$

Q. A ball of mass $5\text{kg}$ moving at speed $2\text{m/s}$ makes a head on collision with an identical ball at rest. The velocities of the balls after the perfectly elastic collision between them are respectively:-

1. $1.2\text{m/s},0.5\text{m/s}$
2. $1\text{m/s},1\text{m/s}$
3. $0\text{m/s},2\text{m/s}$
4. $1.5\text{m/s},0.2\text{m/s}$

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. 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. Assertion: In elastic collision, kinetic energy is conserved
Reason: Energy is always conserved.
MY PROBLEM
According to book Answer is (b) [both are true but reason is not the explanation of assertion]
​​​​​​ Assertion is true but I think reason is false because Energy is conserved only in elastic collision and in Reason it is not mentioned whether it is elastic or inelastic.

Q. Particle A makes a perfectly elastic collision with another particle B at rest.They fly apart in opposite direction with equal speeds.If their masses are Ma and Mb respectively .Then find relation between them

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. 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. A ball is moving with velocity $5\text{m/s}$ towards a heavy wall which is at rest as shown in figure. Assuming collision to be perfectly elastic, find the velocity of the ball immediately after the collision.

1. $0\text{m/s}$ towards left
2. $5\text{m/s}$ towards right.
3. $\frac{5}{2}\text{m/s}$ towards left.
4. $5\text{m/s}$ towards left

Q.

If the kinetic energy of a body of mass $0.1kg$ is $20J$, then find the velocity of that body.

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. This question has statement I and Statement II. Of the four choices given after the Statements, choose the
one that best describes the two Statements.

$\text{Statement-I}:$ A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass
$M$. If the maximum energy loss possible is given as $f\left(\frac{1}{2}m{v}^2\right)\text{then}f=\left(\frac{m}{M+m}\right)$.

$\text{Statement-II}:$ Maximum energy loss occurs when the particles get stuck together as a result of the collision.

1. Statement-I is true, Statement-II is true, Statement-II is the correct explanation of Statement -I.
2. Statement-I is false, Statement-II is true.
3. Statement I is true, Statement-II is false.
4. Statement-I is true, Statement-II is true, Statement-II is not the correct explanation of Statement.

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. $v_2$

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

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.

The kinetic energy of the body will become eight times if

1. Its mass is made four times

2. Its velocity is made four times

3. Both the mass and velocity are doubled

4. Both the mass and velocity are made four times

Q.

Two bodies with kinetic energies in the ratio $4:1$ are moving with equal linear momentum. The ratio of their masses is?

1. $1:2$

2. $1:1$

3. $4:1$

4. $1:4$

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. 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. A small particle of mass m hits a spherical ball of mass M at speed of $V_0$ as shown in the figure. The coefficient of restitution between particle and sphere is 1 and that between sphere and horizontal surface is 0. Then, (given$\frac{M}{m}=3$ and $\theta ={37}^{\circ }$)

1. speed of sphere after collision is $\frac{24V_0}{91}$.
2. impulse on particle by ball is $\frac{90m{V}_0}{91}$.
3. speed of particle after collision is equal to $V_0$.
4. speed of sphere after collision is $\frac{37V_0}{91}$.

Q. A block of mass $(M=1kg)$ is kept on smooth floor of a truck. One end of a spring of force constant $100N/m$ is attached to the block and other end is attached to the body of truck as shown in the figure. At $t=0$, truck begin to move with constant acceleration $2{\text{m/s}}^2$.

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. A body of mass 'm' moving with a speed 'v' suffers an inelastic collision with another body of 'M' at rest and sticks to it, the ratio of the final kinetic energy of the system to the initial kinetic energy is

1. $\left(\frac{m}{m+M}\right)$
2. $\left(\frac{M}{m+M}\right)$
3. $\left(\frac{m+M}{m}\right)$
4. $\left(\frac{m+M}{M}\right)$

Q.

The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.

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 identical balls A and B lie on a smooth horizontal surface, which gradually merges into a curve to a height $3.2$m. Ball A is given a velocity $10$m/sec to collide head on with ball B, which then takes up the curved path. The minimum coefficient of restitution 'e' for the collision between A and B, in order that B reaches the highest point C of curve. $(g=10m/se{c}^2)$.

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

Q. A block of mass $2\text{kg}$ moving at $2{\text{ms}}^{-1}$ collides head on inelastically with another block of equal mass kept at rest. Find the maximum loss in kinetic energy due to the collision.

1. $1\text{J}$
2. $2\text{J}$
3. $3\text{J}$
4. $4\text{J}$