Question

The force of gravitation between two point objects each of mass 'm' kept apart by a distance 'a' is 'F'. Find the force of gravitation between them:
(a) if the mass of one of each object is increased by 25% (other factors are kept same).
(b) if the distance of each object is increased by 50% (other factors are kept same).

Answer 1

Given, $F=\frac{G{m}^2}{a^2}$
(a) Final mass of one object is $m+0,25m=1.25m$
Then
$F^{\prime }=\frac{G(1.25m{)}^2}{a^2}=1.5625F$
(b) Final distance between the masses is $=a+0.5a=1.5a$
Then,
$F^{\prime }=\frac{G\times m^2}{(1.5a{)}^2}=\frac{G{m}^2}{2.25(a{)}^2}=\frac{4}{9}F$