Question

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

A. 1/9
B. 1/3
C. 3
D. 9

Answer 1

option A

Step-by-step explanation:

given,

distance between two masses is doubled

new distance, r' = 3 r

using gravitational force equation

`F = (GMm)/(r^2)`............(1)

new gravitational force

`F' = (GMm)/(r'^2)`

now from the given condition

`F' = (GMm)/((3r)^2)`

`F' = (GMm)/(9r^2)`

`F' = (1)/(9)(GMm)/(r^2)`

now, from equation (1)

`F' = (1)/(9)F`

`(F')/(F) = (1)/(9)`

now, the change in gravitational force factor is equal to
`(1)/(9)`

Hence, the correct answer is option A