$A$ ball of mass $m$ moves with speed $v$ and strikes a wall having infinite mass and it returns with the same speed. Then the work done by the ball on the wall is:

$A$ $15 \,g$ ball is shot from a spring gun whose spring has a force constant of $600 \,N/m$. The spring is compressed by $5 \,cm$. The greatest possible horizontal range of the ball for this compression is .... $m$ $(g = 10 \,m/s^2)$ (in $.0$)

$A$ small bucket of mass $M \, kg$ is attached to a non-extensible string of length $L \, m$. The bucket is released from rest when the string is in a horizontal position. At its lowest point,the bucket scoops up $m \, kg$ of water and rises to a height $h$. The height $h$ (in meters) is:

$A$ body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x$ cm into the sand,then the average resistance offered by the sand to the body is

In two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3:1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Find the ratio between the relative velocity of approach and the relative velocity of separation in the second collision.

Block $A$ of mass $m$ is hanging from a vertical spring of spring constant $k$ and is at rest. Block $B$ of mass $m$ strikes block $A$ with velocity $v$ and sticks to it. The velocity $v$ for which the spring just attains its natural length is: