Two solid spheres of same size of a certain metal are placed in contact with each other. The relation between gravitational force and radius is

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$\frac{7}{9} (G π^{2} ρ^{2}) R^{4}$

$\frac{2}{9} (G π^{2} ρ^{2}) R^{4}$

$\frac{4}{9} (G π^{2} ρ^{2}) R^{4}$

$\frac{5}{9} (G π^{2} ρ^{2}) R^{4}$

answer is A.

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Detailed Solution

The weights of the spheres may be assumed to be concentrated at their centres.
So $F = \frac{G [\frac{4}{3} {πR}^{3} ρ] \times [\frac{4}{3} {πR}^{3} ρ]}{{(2 R)}^{2}} = \frac{4}{9} (G π^{2} ρ^{2}) R^{4} ∴ F \propto R^{4}$

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