Question

the gravitational force between two bodies is 1 Newton if the distance between them is doubled what will be the force between them?

Answer 1

The force will be decreased by 4 times.

Answer 2

New force, $F'=\dfrac{1}{4}\times F$

Explanation:

The gravitational force between two bodies is given by :

$F=G\dfrac{m_1m_2}{d^2}$

d is the distance between two masses

$F\propto \dfrac{1}{d^2}$

$F=\dfrac{k}{d^2}$

if distance between them is doubled, d' = 2d

$F'=\dfrac{k}{d'^2}$

$F'=\dfrac{k}{(2d)^2}$

$F'=\dfrac{1}{4}\times \dfrac{k}{d^2}$

$F'=\dfrac{1}{4}\times F$

So, the new force becomes (1/4)th of the initial force.

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