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If two bodies P and Q having masses $m_{1}$ and $m_{2}$ , separated by a distance $d_{1}$ exerts a force $F$ on each other. Is it true that the force will be $4 F$ if the masses of both bodies are doubled?

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False

answer is A.

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Detailed Solution

The above statement is True.
We know by formula of Force due to gravitation,

F = \frac{G m_{1} m_{2}}{d^{2}}

, that for having constant distance between the bodies the gravity force is directly proportional to the product of their masses.
Given:
Mass of both the bodies are doubled,

= 2 m_{1} {2 m}_{2}

So the force will be,

F_{1} = \frac{G {\times 2 m}_{1} \times 2 m_{2}}{d^{2}}

\Rightarrow

= \frac{4 \times G m_{1} m_{2}}{d^{2}}

\Rightarrow

= 4 \times F

\Rightarrow

F_{1} = 4 F

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