A rope ladder of length L is attached to a balloon of mass M. As the man of mass m climbs the ladder into the balloon basket, the balloon comes down by a vertical distance s. Then the increase in potential energy of man divided by the increase in potential energy of balloon is

Options

A. `(L-s)/(s)`
B. `L/s`
C. `(s)/(L-s)`
D. `L-s`

Answer

A

Explanation

Work done by man, `mgL=mg(L-s)+mgs`
where `mg(L-s)` is the increase in potential energy of the man and `mgs` is the increase in potential energy of the balloon because the balloon would have been lifted up but for the climbing of the man. So
Increase in PE of man/Increase in PE of balloon=`(mg(L-s))/(mgs)-(L-s)/(s)`