$A$ body falls from a height of $10 \ m$ onto the ground and rebounds to a height of $2.5 \ m$. Find the ratio of the velocity of the body just before the collision and just after the collision.

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

$A$ bullet of mass $10 \,g$ moving with a speed of $20 \,m/s$ hits an ice block of mass $990 \,g$ kept on a frictionless floor and gets stuck in it. How much ice will melt if $50 \%$ of the lost kinetic energy $(KE)$ goes to the ice? (Initial temperature of the ice block and bullet $= 0^{\circ}C$,Latent heat of fusion of ice $L = 80 \,cal/g = 336 \,J/g$)

$A$ ball impinges directly on a similar ball of same mass at rest. If $1/4$ of the kinetic energy is lost by the impact,the value of the coefficient of restitution is

$A$ body is dropped on the ground from a height $h_1$ and after hitting the ground,it rebounds to a height $h_2$. If the ratio of velocities of the body just before and after hitting the ground is $4$,then the percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ is $.......$

$A$ body of mass $m$ moving with velocity $v$ collides inelastically with another body of the same mass. After the collision,the first body moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. What will be the speed of the second body after the collision?