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Two identical spheres are placed in contact with each other. The force of gravitation between two spheres will be proportional to (R = radius of each sphere)

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$R^{2}$

$R^{- 2}$

$R^{4}$

$R^{- 4}$

answer is C.

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Detailed Solution

$F = G \cdot \frac{m^{2}}{r^{2}}$

$\begin{aligned} F = \frac{G {(\frac{4}{3} π R^{3} ρ)}^{2}}{(2 R)^{2}} \\ F = \frac{G {(\frac{4}{3} π ρ)}^{2} R^{6}}{4 R^{2}} \end{aligned}$

$\Rightarrow F \propto R^{4}$

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