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. Increases by mg (l - h)
• B. Increases by mgl
• C. Increases by mgh
• D. Increases by mg (2l - h)

Answer 1

The correct option is A Increases by mg (l - h)

Work done by man $=mgl$

Balloon descends by $h$

Gain of PE of man $=mgl-mgh$

The work done goes as gain in PE

$\Rightarrow mgl=mgh+E$

Potential energy of man increases by $mg(l-h).$

Hence, the answer is increases by $mg(l-h).$