Write the dimensional formula of $\frac {k}{m}$.

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 vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d.$ The net work done in the process is

An engine is attached to a wagon through a shock absorber of length $1.5\,m$. The system with a total mass of $50,000 \,kg$ is moving with a speed of $36\, km\,h^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0\,m$.

If $90\%$ of energy of the wagon is lost due to friction, calculate the spring constant.

Inside a lift, a spring (Force constant $k = 1000\ N/m$) and block ($mass = 1\  kg$) are both in a state of rest. Now the lift suddenly starts moving upwards with acceleration $a = g$. Find the maximum total compression in the spring in centimeter. ($g =10\ m/s^2$) :-

Two plates each of mass $m$ are connected by a massless spring as shown below. A weight $w$ is put on the upper plate which compresses the spring further. When $w$ is removed, the entire assembly jumps up. The minimum weight $w$ needed for the assembly to jump up when the weight is removed is just more than ...........$ \,m$