$A$ ball falls freely from rest from a height of $6.25 \ m$ onto a hard horizontal surface. If the ball reaches a height of $81 \ cm$ after the second bounce from the surface,the coefficient of restitution is

$A$ body falls freely onto a hard horizontal surface. If the coefficient of restitution between the surface and the body is $e = 0.8$,then the ratio of the maximum height to which the body rises after the second impact to the initial height of the body is:

$A$ ball is dropped from a height of $5\,m$. The time after which the ball stops rebounding,if the coefficient of restitution between the ball and the ground is $e = 1/2$,is ............. $s$.

$A$ bullet of mass $0.01\, kg$ travelling at a speed of $500\, m/s$ strikes and passes horizontally through a block of mass $2\, kg$ which is suspended by a string of length $5\, m$. The centre of gravity of the block is found to rise a vertical distance of $0.1\, m$. What is the speed of the bullet after it emerges from the block? (The time of passing of the bullet is negligible,$g = 9.8\, m/s^2$)

$A$ smooth sphere is moving on a horizontal surface with a velocity vector $(2 \hat{i} + 2 \hat{j}) \ m/s$ immediately before it hits a vertical wall. The wall is parallel to the vector $\hat{j}$ and the coefficient of restitution between the sphere and the wall is $e = 1/2$. The velocity of the sphere after it hits the wall is:

Two identical balls $A$ and $B$ of equal mass $m$ are lying on a smooth surface as shown in the figure. If ball $A$ hits ball $B$ at rest with a velocity $16 \,ms^{-1}$,then the coefficient of restitution $e$ between $A$ and $B$ so that $B$ just reaches the highest point of the smooth inclined plane of height $5 \,m$ is $\left(g=10 \,ms^{-2}\right)$