Question

A rope ladder with a length $l$ metres 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. In this case, the potential energy of the balloon:

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

Answer 1

Answer: (B)

increases by $mgh$

The formula for potential energy due to gravity is $PE=mgh$.

The total work done by the man is given as $mgl$ where $l$ is the length of the ladder.

As the man moves up the rope, the balloon descends a height h.
So, gain in potential energy of the man is $mgl-mgh$.
If $dE$ be the change in potential energy of the balloon, then by conservation of energy,

Total Work done = Change in Potential energy of the system.

So, we have,
$mgl=mgl-mgh+dE$.

That is, $dE=mgh$.
Hence, the potential energy of the balloon increases by mgh.