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 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

A spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring some elongation and released.

Pulley and spring are massless and the friction is absent everwhere. $5\, kg$ block is  released from rest. The speed of $5\, kg$ block when $2\, kg$ block leaves the contact  with ground is (take force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2)$

In a spring gun having spring constant $100\, {N} / {m}$ a small ball $'B'$ of mass $100\, {g}$ is put in its barrel (as shown in figure) by compressing the spring through $0.05\, {m}$. There should be a box placed at a distance $'d'$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2\, {m}$ above the ground. The value of $d$ is $....{m} .$ $\left(g=10\, {m} / {s}^{2}\right)$

A spring with spring constant k when stretched through $1\, cm$, the potential energy is $U$. If it is stretched by $4 \,cm.$ The potential energy will be