Question

Distance between 2 bodies is increased to 3 times its original value. What is the effect on gravitational force between them

Answer 1

As Force is inversely proportional to distance square , when the distance is increased to three time the force between them decreases by NINE times.

Answer 2

New force becomes (1/9)th times of the initial force.

Explanation:

The gravitational force acting between two bodies is given by :

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

r is the distance between two bodies

It is mentioned that, distance between 2 bodies is increased to 3 times its original value, r' = 3r

New gravitational force is given by :

$F'=G\dfrac{m_1m_2}{r'^2}$

$F'=G\dfrac{m_1m_2}{(3r)^2}$

$F'=\dfrac{1}{9}\times G\dfrac{m_1m_2}{r^2}$

$F'=\dfrac{1}{9}\times F$

New force becomes (1/9)th times of the initial force.

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