Question

How is the gravitational force between two bodies affected when distance between them is halved

Answer 1

Gravitational force between two objects varies inversely with the distance raised to the power 2.
or, $F \propto \dfrac{1}{r^2}$

$\dfrac{F_1}{F_2} = \dfrac{{r_2}^2}{{r_1}^2}$ ......(1)
where, $r_2 = 2r_1$
So, (1) becomes,

$\dfrac{F_1}{F_2} = \dfrac{{2r_1}^2}{{r_1}^2}$
or, $\dfrac{F_1}{F_2} = 2^2$
or, $\dfrac{F_1}{F_2} = 4$
or, $\dfrac{F_2}{F_1} = \dfrac14$

So, the force becomes 1/4 th compared to before.

Here $F_1, F_2, r_1, r_2$ are initial and final force and distance respectively.

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