$A$ ball after falling from a height of $10 \ m$ strikes the roof of a lift which is descending with a velocity of $1 \ m/s$. The recoil velocity of the ball will be ............. $m/s$. (Assume elastic collision)

$A$ 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.

During an elastic collision between two bodies,which of the following statements are correct?
$I$. The initial kinetic energy is equal to the final kinetic energy of the system.
$II$. The linear momentum is conserved.
$III$. The kinetic energy during $\Delta t$ (the collision time) is not conserved.

$A$ 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 falling on the ground from a height of $10 \, m$,rebounds to a height of $2.5 \, m$. The ratio of the velocities of the body just before and after the collision will be:

$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$.