$A$ ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a stationary ball of mass $nm$. What is the fraction of the kinetic energy transferred to the heavier ball?

$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. The ratio of the $K.E.$ of the colliding body before and after the collision will be: (in $: 1$)

After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

$A$ 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

Two smooth objects with a coefficient of restitution $e$ collide directly and bounce as shown. Newton's law of restitution gives: