Question

If the distance between two masses is tripled, the gravitational force between changes by a factor of:_______

Answer 1

Answer:

option A

Explanation:

given,

distance between two masses is doubled

new distance, r' = 3 r

using gravitational force equation

$F = \dfrac{GMm}{r^2}$............(1)

new gravitational force

$F' = \dfrac{GMm}{r'^2}$

now from the given condition

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

$F' = \dfrac{GMm}{9r^2}$

$F' = \dfrac{1}{9}\dfrac{GMm}{r^2}$

now, from equation (1)

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

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

now, the change in gravitational force factor is equal to $\dfrac{1}{9}$

Hence, the correct answer is option A