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Q.

Two metal spheres each of radius ‘r’ and made of same material are separated by a certain fixed distance d $(d > 2 r)$ in a medium. The gravitational force between those spheres is proportional to

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a

$r^{6}$

b

$r^{4}$

c

$\frac{1}{r^{4}}$

d

$\frac{1}{r^{2}}$

answer is D.

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Detailed Solution

If 'm' is the mass of each sphere,
$\begin{array}{l} m = \frac{4}{3} {πr}^{3} ρ \\ ∴ F = \frac{{Gm}_{1} m_{2}}{d^{2}} = \frac{G {(\frac{4}{3} {πr}^{3} ρ)}^{2}}{d^{2}} \\ \Rightarrow F \propto r^{6} \end{array}$

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Two metal spheres each of radius ‘r’ and made of same material are separated by a certain fixed distance d (d>2r) in a medium. The gravitational force between those spheres is proportional to