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Distance

If F is the...

Question

If $F$ is the force between two bodies of masses $m_{1}$ and $m_{2}$ at certain separation, then what is the force between $\sqrt{5} m_{1}$ and $\sqrt{3} m_{2}$ at the same separation?

\sqrt{5} F

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F / \sqrt{15}

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\sqrt{15} F

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F

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Solution

The correct option is C $\sqrt{15} F$
$F = \frac{G m_{1} m_{2}}{r^{2}}$
Where r is the distance between $m_{1}$ and $m_{2}$
If $m_{1} \to \sqrt{5} m_{1}$
$m_{2} \to \sqrt{3} m_{2}$
$∴ F^{'} = \frac{G \sqrt{5} m_{1} \sqrt{3} m_{2}}{r^{2}}$
$= \sqrt{15} \frac{G m_{1} m_{2}}{r^{2}} = \sqrt{15} F$

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The gravitational force between two point masses $m_{1}$ and $m_{2}$ at separation r is given by $F = k \frac{m_{1} m_{2}}{r^{2}}$ The constant k

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