Question

A mass $2m$ rests on a horizontal table. It is attached to a light inextensible string which passes over a smooth pulley and carries a mass $m$ at the other end. If the mass $m$ is raised vertically to a height $h$ and is then dropped, what is the speed with which the mass $2m$ begins to rise?

Answer 1

Velocity of the mass $m$ just before string becomes tight.

$\nu =\sqrt{2gh}$ (i)

using impulse = change in momentum

For mass $2m$

$J=2m{\nu }_1$ (ii)

For mass $m$ (iii)

$m\nu -J=m{\nu }_1$

Solving Eqs. (i), (ii) and (iii), we get $\nu =\frac{\sqrt{2gh}}{3}$