Question

A balloon with a rope ladder hanging from it has a mass 4m. With a boy of mass m at the lowest rung of the ladder, the balloon is floating in equilibrium in the sky. The boy climbs the ladder of length L reaching its top. If g is acceleration due to gravity, then the gain in the gravitational potential energy of the boy is

• A. mgL
• B. 0.75mgL
• C. 0.8mgL
• D. zero

Answer 1

The correct option is C

0.8mgL

As the boy moves up a distance 'L' , say the balloon - ladder - boy system comes down a distance 'x' .

This is because the internal forces cannot shift the centre of mass

$\therefore$Displacement of boy w.r.to ground = L - x

Displacement of balloon w.r.to ground =(-x)

Displacement of centre of mass $△x_{cm}$ = 0

$\therefore △x_{cm}=\frac{m_1△x_1+m_2△x_2}{m_1+m_2}$

$\Rightarrow 0=\frac{m(L-x)+4m(-x)}{5m}\Rightarrow x=\frac{L}{5}$

$\therefore$Displacement of boy w.r.to ground = L - x = L - $\frac{L}{5}$ = 0.8L

$\therefore$ Gain in potential energy of the boy = (0.8)mgL