Question

What happens to the gravitational force between two objects when the distance between them is :
(1) doubled ?
(2) halved ?

Answer 1

`F = (GMm)/r^2`
where,
F − gravitational force
G − gravitational constant
M − mass of the earth
m − mass of object
r − distance

(i).  r = doubled
`F = (GMm)/r^2` keeping everything constant i.e. G, M, m
= `(GMm)/(2r)^2`
= `(GMm)/(4r^2)`
F becomes one-fourth.

(ii) r = halved
`F = (GMm)/r^2`  keeping everything constant i.e. G, M, m
= `(GMm)/(1/(2r))^2`
= `(GMm)/(1/(4r))^2`
= `(4GM  m)/(r^2)`
F becomes four times the original.