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Having increased the distance between masses of two objects by five times; in order to maintain the same gravitational force, the mass of one of them have to be increased by [[1]] times.

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Detailed Solution

Having increased the distance between masses of two objects by five times; in order to maintain the same gravitational force, the mass of one of them has to be increased by

25

times.
Let the Mass of two objects be

m_{1} and m_{2} .

Let the mass of the two objects after increasing the distance between them by five times be

m_{3} and m_{4}

Then, by the universal law of gravity

F 1 = \frac{G (m_{1} m_{2})}{{(d)}^{2}} = \frac{G (m_{3} m_{4})}{{(5 d)}^{2}}

(from the given question)

\Rightarrow 25 m_{1} m_{2} = m_{3} m_{4}

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