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Two equal masses separated by a certain distance experience a force $F$ . Now, the masses are doubled. To maintain the same force, the ratio of the new separation of distance and the previous separation of distance should be [[1]].

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Detailed Solution

Two equal masses separated by a certain distance experience a force

F

. Now, the masses are doubled. To maintain the same force, the ratio of the new separation of distance and the previous separation of distance should be

2

.
According to Newton's law of gravitation, the force between two masses is given by,

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

…………… (1)
Where,

F = original force

G = gravitational constant

m_{1} and m_{2} = masses of object

r = distance between objects

Given,

F = F^{'}

, where,

F^{'}

is the force after doubling the masses
Therefore, if the new separation of distance is

r^{'}

So,

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

\Rightarrow ({r')}^{2} = 4 r^{2}

\frac{r'}{r} = 2

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