$A$ ball is dropped from a height of $20\,m$. If the coefficient of restitution for the collision between ball and floor is $0.5$,after hitting the floor,the ball rebounds to a height of $.............m$.

$A$ ball strikes a horizontal surface as shown in the figure. If the coefficient of restitution is $e = 1/\sqrt{3}$,then the angle $\theta$ is ............... $^o$.

$A$ sphere strikes a wall and rebounds with a coefficient of restitution $e = 1/3$. If it rebounds with a velocity of $0.1 \ m/s$ at an angle of $60^{\circ}$ to the normal to the wall,the percentage loss of kinetic energy is:

$A$ body falls from a height of $10 \ m$ onto the ground and rebounds to a height of $2.5 \ m$. The percentage loss in kinetic energy 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 moving with velocity $2 \,m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be: