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Universal Law of Gravitation

If F is the f...

Question

If F is the force between two bodies of masses $m_{1}$ and $m_{2}$ at certain separation. Find the force between $\sqrt{2} m_{1}$ and $\sqrt{3} m_{2}$ at same separation.

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Solution

Force due to gravity is given by $\frac{G m_{1} m_{2}}{r^{2}}$

now, if $\frac{G m_{1} m_{2}}{r^{2}} = F$ is given, then

$\frac{G (\sqrt{2} m_{1}) (\sqrt{3} m_{2})}{r^{2}} = \sqrt{6} . F$ . ( $∵$ r and G is constant for both the cases).

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