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Q.

If the distance between two objects is increased four times, then by how many times should the mass of one of the objects be increased to maintain the same gravitational force?

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a

4

times

b

8

times

c

16

times

d

32

times

answer is C.

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Detailed Solution

If the distance between two objects is increased four times, then masses must be increased

16

times.
“Newton’s Law of Gravitation states that the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” The formula that gives this force is,

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

where G is the universal Gravitation constant.
If the distance is increased

4

times that introduces a factor of

4^{2}

in the denominator, to cancel that out, one of the masses must be increased

16

times so that the gravitational force between them remains the same.

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If the distance between two objects is increased four times, then by how many times should the mass of one of the objects be increased to maintain the same gravitational force?