A rain drop of radius ‘r’ falls from a certain height ‘h’ above the ground. The work done by the gravitational force is proportional to

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A rain drop of radius ‘r’ falls from a certain height ‘h’ above the ground. The work done by the gravitational force is proportional to

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r^{4}

r^{3}

r^{2}

answer is B.

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Detailed Solution

m_{1} =

mass of rain drop

$m_{2} =$ mass of earth

r = radius of rain drop

$F = \frac{{Gm}_{1} m_{2}}{r^{2}}$

$F = \frac{G . ρ . \frac{4}{3} π r^{3} \times m_{2}}{h^{2}}$

$(∵ G, ρ, \frac{4}{3} π, m_{2} are constant)$

$\begin{matrix} F \propto r^{3} \end{matrix}$

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