When the masses of two bodies are doubled and the separation between them is halved, the effect they have on the gravitational force between them is

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The gravitational force will increase by

16

times.

The gravitational force will increase by

3

times.

The gravitational force will increase by

10

times.

The gravitational force will decrease by

12

times.

answer is A.

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Detailed Solution

The new gravitational force will increase by

16

times as compared to the original gravitational force.
Newton’s law of gravitation states that “every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.”
Therefore, the gravitational force is given by

F = G \frac{M_{1} M_{2}}{R^{2}}

….. (1)
Here,

G

is the universal gravitational constant

R

is the distance between two bodies
The masses of the bodies are represented by

M_{1}

and

M_{2}

According to the given data,

R_{1} = \frac{R}{2}

and also, the masses of two bodies are doubled.
Thus, we get

F_{1} = G \frac{{2 M}_{1} \times 2 M_{2}}{{(\frac{R}{2})}^{2}}

By simplifying, we get

F_{1} = G \frac{{4 M}_{1} M_{2}}{\frac{1}{4} {(R)}^{2}}

\Rightarrow F_{1} = G \frac{{4 M}_{1} M_{2}}{{(R)}^{2}} \times \frac{4}{1}

\Rightarrow F_{1} = 16 G \frac{M_{1} M_{2}}{{(R)}^{2}}

From equation (1), we get

F_{1} = 16 F

This indicates that when the masses of two bodies are doubled and separation between them is halved, then the new gravitational force will increase by 16 times the original gravitational force.

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