The distance between two objects is reduced to half then the gravitational force between two objects becomes:

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3 F

4 F

5 F

None of these

answer is B.

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Detailed Solution

The distance between two objects is reduced to half then the gravitational force between two objects becomes

4 F

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

,where

G =

universal gravitation constant,

m_{1} =

mass of first object,

m_{2} =

mass of second object and

r =

distance between them
So, when the distance between them becomes half i.e.

r^{'} = \frac{r}{2}

, the value of force will change as

F' = \frac{G (m_{1}) {(m}_{2})}{\frac{r^{2}}{4}}

\Rightarrow F' = \frac{4 G (m_{1}) {(m}_{2})}{r^{2}}

Therefore,

F^{'} = 4 F

, so the force becomes 4 times its original value.

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