Question

A ladder of length l carrying a man of mass m at its end is attached to the basket of a balloon of mask 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
A.mgl
B.mgh
C.mg
D.mg (l-h)

Answer 1

This problem can be solved using the formula for work done. To calculate the work done by the man you have to calculate the potential energy as work done is equal to the negative change in the potential energy. So, initially find the change in height. Substitute the value in formula for potential energy. Then, take the negative value of this potential energy and equate it with the work done. Thus, you will get the work done by the man.

Complete answer:
When the man climbs up the ladder of length l into the balloon, the balloon descends by a height h. Thus, the net height gained by the man is,
$H= h-l$ …(1)
We know, potential energy is given by,
$P.E.= mgH$ …(2)
The increase in the potential energy of the man can be given by substituting equation. (2) in equation. (1)
$\therefore \Delta P.E. = mg(h-l)$
Now, we know, work done is equal to the negative increase in the potential energy.
$\therefore W= -\Delta P.E.$
$\therefore W= -mg(h-l)$
$\therefore W= mg(l-h)$
Thus, the work done by the man is mg(l-h).

Hence, the correct answer is option D i.e. mg(l-h).

Note:
According to the Work-energy theorem, change in Kinetic energy of a body is equal to the work done on the body. Negative change in the potential energy is equal to the work done on the body. Work done by a conservative force only depends on the initial and final position of the body. It does not depend on the path taken. Popular examples of conservative forces are Gravitational force and Electrostatic force. Work done by a non-conservative force depends on the path taken by the body. Non-frictional force is an example of non-conservative force.