If the attractive force between two bodies of mass $M_{1}$ and $M_{2}$ and situated at a distance R is F, then find the force F' between them at distance (R+d) in terms of F.

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Solution

According to Newton's law of gravitation,
$F = \frac{G M_{1} M_{2}}{R^{2}}$ ;
$F^{|} = \frac{G M_{1} M_{2}}{(R + d)^{2}}$
$∴ \frac{F^{|}}{F} = \frac{R^{2}}{(R + d)^{2}};$
$∴ F^{|} = \frac{R^{2} F}{(R + d)^{2}}$

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