Question

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 potential energy of the man
A. (a) Increases by `mg(l-h)`
B. (b) Increases by `mgl`
C. (c) Increases by `mgh`
D. (d) Increases by `mg(2l-h)`

Answer 1

Correct Answer - A
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`