Gravitational Force Ratio

Question

If distance between two masses doubles, gravitational force becomes?

RankGuru · Accepted Answer

1. **Newton's Law**: The force $F = G \frac{Mm}{r^2}$, meaning $F \propto \frac{1}{r^2}$.
2. **Scenario**: The distance $r$ is doubled ($r' = 2r$).
3. **Substitute**: $F' = G \frac{Mm}{(2r)^2} = \frac{GMm}{4r^2}$.
4. **Compare**: $F' = \frac{1}{4} F$.
5. **Result**: The force becomes **one-fourth** or a quarter of its original value due to the inverse square dependence on distance.

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Gravitational Force Ratio

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