Two perfectly elastic particles $P$ and $Q$ of equal mass are travelling along the line joining them with velocities $15 \ m/s$ and $10 \ m/s$ respectively. After a perfectly elastic collision,their velocities (in $m/s$) will be:

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. What is the loss in kinetic energy of the colliding body?

$A$ ball is dropped from a height of $10 \ m$ and hits the roof of an elevator moving downwards with a velocity of $1 \ m/s$. What is the rebound velocity of the ball in $m/s$?

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

$A$ smooth sphere $A$ moves on a frictionless horizontal surface with an angular velocity $\omega$ and a linear velocity $v$ of its center of mass. It undergoes an elastic collision with another identical sphere $B$ at rest. Neglecting friction everywhere,if the angular speeds after the collision are $\omega_A$ and $\omega_B$ respectively,then:

Two identical spheres move in opposite directions with speeds $v_1$ and $v_2$ and pass behind an opaque screen,where they may either cross without touching (Event $1$) or make an elastic head-on collision (Event $2$).