$A$ ball of mass $m$ moving with a speed $u$ undergoes a head-on elastic collision with a ball of mass $nm$ initially at rest. The fraction of the incident energy transferred to the heavier ball is

$A$ body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$,which is at rest. The collision is head-on and elastic in nature. After the collision,the fraction of energy lost by the colliding body $A$ is

$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

$A$ ball $A$ of mass $m$ moving along the positive $x$-direction with kinetic energy $K$ and momentum $p$ undergoes an elastic head-on collision with a stationary ball $B$ of mass $M$. After the collision,the ball $A$ moves along the negative $x$-direction with kinetic energy $K/9$. The final momentum of $B$ is:

Collision takes place between two solid spheres denoted as $1$ and $2$. The initial velocities of the spheres are $u_1 = 3 \ m/s$ and $u_2 = 1.5 \ m/s$,and the final velocities are $v_1 = 2.5 \ m/s$ and $v_2 = 3.5 \ m/s$. The coefficient of restitution between the materials of the spheres is nearly:

$A$ ball of mass $2m$ and a system of two balls with equal masses $m$ connected by a massless spring are placed on a smooth horizontal surface (see figure). Initially, the ball of mass $2m$ moves with velocity $u_0$ along the line passing through the centres of all the balls and the spring, whereas the system of two balls is at rest. Assuming that the collision between the individual balls is perfectly elastic, the ratio of vibrational energy stored in the system of two connected balls to the initial kinetic energy of the ball of mass $2m$ is