Answer:
option A
Explanation:
given,
distance between two masses is doubled
new distance, r' = 3 r
using gravitational force equation
[tex]F = \dfrac{GMm}{r^2}[/tex]............(1)
new gravitational force
[tex]F' = \dfrac{GMm}{r'^2}[/tex]
now from the given condition
[tex]F' = \dfrac{GMm}{(3r)^2}[/tex]
[tex]F' = \dfrac{GMm}{9r^2}[/tex]
[tex]F' = \dfrac{1}{9}\dfrac{GMm}{r^2}[/tex]
now, from equation (1)
[tex]F' = \dfrac{1}{9}F[/tex]
[tex]\dfrac{F'}{F} = \dfrac{1}{9}[/tex]
now, the change in gravitational force factor is equal to [tex]\dfrac{1}{9}[/tex]
Hence, the correct answer is option A
