$A$ ball moving with velocity $V$ undergoes a perfectly elastic collision with an identical ball moving in the opposite direction with velocity $2V$. Taking the direction of $V$ as positive,find the velocities of both balls after the collision.

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic,which of the following figure is a possible result after collision?

As per the given figure,a small ball $P$ slides down the quadrant of a circle and hits another ball $Q$ of equal mass which is initially at rest. Neglecting the effect of friction and assuming the collision to be elastic,the velocity of ball $Q$ after the collision will be $............\,m/s$ $(g = 10\,m/s^2)$.

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$. Three identical spheres of same mass undergo one-dimensional motion as shown in the figure with initial velocities $v_{A} = 5 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 4 \ m/s$. If we wait sufficiently long for elastic collisions to happen,then $v_{A} = 4 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 5 \ m/s$ will be the final velocities.
Reason $(R)$: In an elastic collision between identical masses,two objects exchange their velocities. In the light of the above statements,choose the correct answer from the options given below:

$A$ body of mass $M$ moving at speed $V_{0}$ collides elastically with a mass $m$ at rest. After the collision,the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass $M$. The largest possible value of the ratio $M/m$,for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal,is:

$A$ particle of mass $m$ moving with velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a very short time $T$. Their force of interaction increases from zero to $F_0$ linearly in time $T/2$, and decreases linearly to zero in further time $T/2$. The magnitude of $F_0$ is