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The force of gravitation between two objects changes [[1]] times when the distance between them is reduced to half.

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Detailed Solution

The force of gravitation between two objects changes

4

times when the distance between them is reduced to half.
It is known that the force of gravitation between two objects is given by

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

Where

F

G

r

m_{1}

and

m_{2}

are the gravitational force, universal gravitational constant, radius, mass of the first body and mass of the second body respectively.
If the distance is reduced to half, i.e.,

r^{'} = r / 2

, then the new force of gravitation is given by

\Rightarrow {F'}^{'} = G \frac{m_{1} m_{2}}{{r^{'}}^{2}}

\Rightarrow F' = G \frac{m_{1} m_{2}}{{(r / 2)}^{2}}

\Rightarrow F' = G \frac{m_{1} m_{2}}{r^{2}}

\Rightarrow F' = 4 F

Hence, the force of gravitation becomes four times.

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