A box is put on a scale which is adjusted to read zero, when the box is empty. A stream of pebbles is then poured into the box from a height h above its bottom at a rate of n pebbles. Each pebble has a mass m. If the pebbles collide with the box such that they immediately come to rest after collision, the scale reading at time t after the pebbles begin to fill the box is

Given the rate of pebbles =n, 

thus the number of pebbles in the box after time ′t′=nt

and weight of the pebble in the box after time t =mgnt

where m= mass, g= acceleration due to gravity.

Also given the height of fall=h

Now from the equation of motion, we have,

$\mathrm{h} = \mathrm{ut} + \frac{1}{2}{\mathrm{gt}}^2$ 

as initial velocity of the pebble =0m/s

$\mathrm{h} = \frac{1}{2}{\mathrm{gt}}^2$

$\mathrm{t} = \sqrt{\frac{2\mathrm{h}}{\mathrm{g}}}$

Also we know,

v=u+gt = gt =$\sqrt{2\mathrm{gh}}$

The momentum of pebble P=mv=$\mathrm{m}\sqrt{2\mathrm{gh}}$

As per the question, pebbles strike at the rate of n, then the force required to stop the pebble will be 

F =nP =$\mathrm{mn}\sqrt{2\mathrm{gh}}$

Thus the reading of the scale at time t after the pebbles begin to fill the box will be 

W = mgnt+F = $\mathrm{mn}\{\sqrt{2\mathrm{gh}} + \mathrm{gt}\}$