Question

What happens to the gravitational force between two objects, if
(i) the mass of one object is doubled?
(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?

Answer 1

$F=\frac{GMm}{R^2}$

$\left(i\right)$

If one mass say, $m$ is doubled, then force is

$F^{\prime }=\frac{2GMm}{R^2}=2F$ the force gets doubled.

$\left(ii\right)$

If the distance is doubled and tripled-

$F^{\prime }=\frac{2GMm}{(2R{)}^2}=\frac{F}{4}$

and,

$F^{\prime }=\frac{2GMm}{(3R{)}^2}=\frac{F}{9}$

$\left(iii\right)$

If both masses are doubled, then force is

$F^{\prime }=\frac{4GMm}{R^2}=4F$ the force gets quadrupled.