Question

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

• A. $\frac{L-s}{s}$
• B. $\frac{L}{s}$
• C. $\frac{s}{L-s}$
• D. $L-s$

Answer 1

The correct option is A $\frac{L-s}{s}$

Since the effective height through which man has moved up is given by $L-s$

Hence, increase in potential energy of man will be given by $mg(L-s)$

Since, balloon's natural tendency was to go upward due to upward buoyancy

force, but it has been dragged down by distance $s$ against this buoyant force,

hence, some potential energy will also get stored in the balloon as $mgs$

$\therefore \frac{IncreaseinP.E.ofman}{IncreaseinP.E.ofballoon}=\frac{mg(L-s)}{mgs}=\frac{L-s}{s}$