The potential energy of a certain spring when stretched through a distance $S$ is $10 \,joule$. The amount of work (in $joule$) that must be done on this spring to stretch it through an additional distance $S$ will be

A block of mass $'m'$ is released from rest at point $A$. The compression in spring, when the speed of block is maximum

Two bodies $A$ and $B$ of mass $m$ and $2\, m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_0$. The spring constant $k$ will be

Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$, such that $K_P > K_Q .$ They are stretched first by the same amount (case $a$), then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as, in case $(a)$ and case $(b)$ respectively

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

Two springs have their force constant as $k_1$ and $k_2 (k_1 > k_2)$. when they are  stretched by the same force