$A$ $1 \,kg$ ball moving at $12 \,ms^{-1}$ collides with a $2 \,kg$ ball moving in the opposite direction at $24 \,ms^{-1}$. If the coefficient of restitution is $2/3$, then their velocities after the collision are

$A$ particle of mass $m$ moving with speed $2v$ collides with a mass $2m$ moving with speed $v$ in the same direction. After the collision,the first mass is stopped completely,while the second one splits into two particles each of mass $m$,which move at an angle of $45^o$ with respect to the original direction. The speed of each of the moving particles will be:

$A$ lead ball of mass $2 \ kg$ moving with a velocity of $1.5 \ ms^{-1}$ collides with a ball of mass $3 \ kg$ at rest. After the collision,the second ball moves with a velocity of $1 \ ms^{-1}$ in the original direction of motion of the first ball. Find $\Delta KE$ in $J$.

An object of mass $m$ moving with velocity $u$ collides with another stationary object of mass $M$ and stops just after the collision. The coefficient of restitution is

$A$ particle of mass $m$ strikes the ground inelastically with a coefficient of restitution $e$. Find the relation between the angles $\theta$ and $\alpha$ as shown in the figure.

$A$ body falls on a surface with a coefficient of restitution of $0.6$ from a height of $1 \, m$. The body rebounds to a height of ........... $m$.