$A$ ball of mass $m$ moving with velocity $V$ makes a head-on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking the direction of $V$ as positive,the velocities of the two balls after the collision are:

$A$ particle of mass $1\, kg$ moving with velocity $1\, m/s$,collides elastically with another particle of mass $m$ initially at rest. In the collision,the particle of mass $1\, kg$ loses $\frac{3}{4}$ of its kinetic energy $(K.E.)$. The value of $m$ 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

$A$ ball of mass $m$ moving with velocity $v$ undergoes an elastic collision with another ball of the same mass $m$ moving in the opposite direction with velocity $2v$. What will be their velocities after the collision?

$A$ steel ball of radius $2 \,cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \,cm$ moving with velocity of $81 \,cm \,s^{-1}$ collides elastically with the ball which is at rest. After collision, the ball with radius of $2 \,cm$ moves with a speed of:

$A$ ball falls from a height of $5\,m$ and strikes the roof of a lift. If at the time of collision,the lift is moving in the upward direction with a velocity of $1\,m/s$,then the velocity with which the ball rebounds after collision will be (assume $e = 1$):