A ladder of length `l` carrying a man of mass `m` at its end is attached to the basket of a balloon of mass M. The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height h.
The work done by the man is

Options

A. (a) `mgl`
B. (b) `mgh`
C. (c) `mg`
D. (d) `mg(l-h)`

Answer

A

Explanation

When the man climbs the ladder of length l, the balloon descends by height h. So net height gained by the man is `l-h`. Hence, gain in potential energy of the man is `mg(l-h)`.
Work done by man: `W_1=mgl`
Inclination in potential energy of balloon=work done by man -increase in potential energy of man, i.e.,
`mgl-mg(l-h)=mgh`