Question

What happens to the forces between two objects, if :

The distance between the objects is doubled?

Answer 1

Step 1: Gravitational force formula:

As we know that gravitational force between two objects is given by

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$

Where G = Gravitational force

M = Mass of object 1

m = Mass of object 2

r = Distance between the two objects

Step 2: When the distance between the objects is doubled

So, New distance = 2r

New force = $\frac{\mathrm{GMm}}{{\left(2\mathrm{r}\right)}^2}$

= $\frac{\mathrm{GMm}}{4{\mathrm{r}}^2}$

= $\frac{1}{4}\times$Old force

Thus, when the distance is doubled, the force becomes $\frac{1}{4}$ times of initial value.