Two metal spheres each of radius 'r ' are kept in contact with each other. If d is the density of the material of the sphere, then gravitational force between those spheres is proportional to

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$d^{2} r^{2}$

$d^{2} r^{4}$

$\frac{d^{2}}{r^{4}}$

$\frac{r^{4}}{d^{2}}$

answer is B.

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Detailed Solution

$\begin{array}{l} F = \frac{{Gmm}_{1} m_{2}}{(2 r)^{2}} \\ F = \frac{G (\frac{4}{3}) {πr}^{3} d \cdot (\frac{4}{3}) {πr}^{3} d}{4 r^{2}} F \propto r^{4} d^{2} \end{array}$

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