Question

A rope ladder with a length $1m$ carrying a man with a mass $m$ at its end is attached to the basket of a balloon with a 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 $h$. Then the potential energy of the man (in $J$):

• A. increases by $mg(1-h)$
• B. increases by $mgl$
• C. increases by $mgh$
• D. increases by $mg(21-h)$

Answer 1

The correct option is A increases by $mg(1-h)$

Given , the man goes a height of 1 m but at the same time the balloon comes down by h m. Which means that the man had gone just $(1-h)$ m above his initial position.
Therefore increase in its potential energy is $m\times g\times (1-h)$ joule.