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

$A$ ball of mass $m$ is attached to the lower end of light vertical spring of force constant $k$. The upper end of the spring is fixed. The ball is released from rest with the spring at its normal (unstretched) length, comes to rest again after descending through a distance $x.$

A block  $'A'$  of mass $M$ moving with speed $u$ collides elastically with block $B$ of mass $m$ which is connected to block $C$ of mass $m$ with a spring. When the compression in spring is maximum the velocity of block $C$ with respect to block $A$ is (neglect friction)

The potential energy of a weight less spring compressed by a distance $ a $ is proportional to

$A$ spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring an elongation less than $\frac{{2\mu mg}}{K}$ but more than $\frac{{\mu mg}}{K}$ and released. Which of the following laws/principles of physics can be applied on the spring block system

A mass of $0.5\,kg$ moving with a speed of $1.5 \,m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50\;N/m$. The maximum compression of the spring would be ............. $\mathrm{m}$