Question

The gravitational force between two objects is 100N .how should the distance between the objects be changed so that force between them becomes 50N?

Answer 1

we know F is directly proportional to 1/r²

there fore
$\frac{f1}{f2} = \frac{{r2}^{2} }{ {r1}^{2} }$
$\sqrt{ \frac{100}{50} } = \frac{r2}{r1}$
r2= √2r1

Answer 2

F = G M m / r^2

F1 = 100 N

G , M , m are constant

then

100 x r^2 = G m M ..( equal to K )

100 x r^2 = K

r = underoot K / 10

now

=K / r'^2

100 r^2 = 50 r'^2

2/ 1 = r'^2 / r^2

distance will be increase

because force ( gravitaional ) is inversely proportional to distance square between them .