Question

What happened to the gravitational force between two objects when the distance between them is
(a) doubled
(b) halved

Answer 1

When the distance is doubled force increases to 4 times...... That is the ans.. For (A)....

when distance is halved the force reduces to its 1/4 th..... That is the ans.. For (B)

Answer 2

Gravitational force is inversely proportional to the square of distance between the objects.
(a) when distance is doubled
F = 1/ d^2
F = 1/ (2d) ^2
F = 1/ 4d^2
So, force reduces to 1/4 th

(b) when distance is halved
F = 1/ d^2
F = 1/ (d/2)^2
F = 1/ d^2 /4
F = 4/d^2
So, force increases 4 times