Question

What happens to gravitational force when distance is doubled?

Answer 1

Answer:

The force is reduced by one-forth.

Explanation:

The gravitational force is proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between their centers of mass. That is

$F = \dfrac{G m_1 m_2}{ d^2 } \, \, .$

If the distance is doubled, the new value of force wil be

$F^{\prime} = \dfrac{G m_1 m_2}{ ( 2 d )^2 } </p><p>= \dfrac{1}{4} \, \dfrac{G m_1 m_2}{ ( d )^2 } </p><p>= \dfrac{F}{4} \, \, .</p><p>\, \, .$

As a general rule, remember the gravitational force is an inverse-square law, so whenever you multiply the distance by some factor $k$, the force will decrease by a factor given by the inverse squared of that factor, or $1/k^2$.