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[118]
Given two objects of mass $M and m$ and the distance between them is $r .$

Is it true that the distance between two objects is reduced to $1 / 4$ , the force between them becomes $16$ times?

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True

False

answer is A.

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Detailed Solution

The above statement is True.
When the distance is reduced to

1 / 4 th

,
Using the formula of gravitational force,

F = G \frac{Mm}{r^{2}}

Where G is the gravitational constant,

M and m

are the mass of the object (given) and

r

is the distance between them (given).

\Rightarrow {F ’}^{} = G \frac{Mm}{((1 / 4 r)^{2}}

\Rightarrow F ’ = 16 G \frac{(Mm)}{r^{2}}

\Rightarrow F ’ = 16 F

The force between the two objects becomes

16 times

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