$A$ body of mass $0.5 \ kg$ moves with a speed of $1.5 \ m/s$ on a smooth horizontal surface. It hits a massless spring with a force constant $k = 50 \ N/m$. What will be the maximum compression of the spring in $m$?

$Assertion$ : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.
$Reason$ : Potential energy of a stretched or compressed spring is proportional to the square of extension or compression.

$A$ spring with force constant $k$ is initially stretched by a distance $x$. If it is further stretched by a distance $y$,the work done during the second stretching is.........

$A$ block $B$ is attached to two unstretched springs $S1$ and $S2$ with spring constants $k$ and $4k$,respectively (see figure $I$). The other ends are attached to identical supports $M1$ and $M2$ which are not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall $1$ by a small distance $x$ (figure $II$) and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is:

$A$ spring $40 \, mm$ long is stretched by the application of a force. If $10 \, N$ force is required to stretch the spring by $1 \, mm$,then the work done in stretching the spring by $40 \, mm$ is ............. $J$.

If a spring is stretched by a force $T$,what is the potential energy stored in the spring? (Given $T$ is the tension/force and $k$ is the spring constant.)