Universal Law Of Gravitation

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Two communication satellites exert a mutual gravitational force F on each other while drifting in space. If the mass of each satellite is doubled and the separation between them is also doubled, what is the new mutual force?

RankGuru · Accepted Answer

The mutual gravitational attraction obeys $F = G\frac{m_1 m_2}{r^2}$, so the force depends on the product of the two masses divided by the square of their separation. When each mass is doubled, the numerator $m_1 m_2$ increases by a factor of $2	imes2 = 4$. Simultaneously doubling the separation multiplies $r^2$ by a factor of $2^2 = 4$ in the denominator. The new force is therefore $F' = G\frac{(2m_1)(2m_2)}{(2r)^2} = G\frac{4 m_1 m_2}{4 r^2} = G\frac{m_1 m_2}{r^2} = F$, leaving the force unchanged. The option $2F$ is wrong because it accounts only for the mass increase and ignores the distance change. The option $F/2$ is wrong as it mismatches the powers of the two effects. The option $4F$ is wrong because it doubles the mass effect while ignoring the denominator entirely. This conceptual cancellation is a classic JEE proportionality test. A sanity check confirms the equal fourfold changes in numerator and denominator exactly offset.

Universal Law Of Gravitation

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