What happens to the gravitational force between two objects,if
$(a)$ the mass of one object is doubled?
$(b)$ the distance between the objects is doubled?
$(c)$ the masses of both the objects are doubled? Give reason in each case.

(N/A) The gravitational force between two objects is given by the expression $F = \frac{G m_1 m_2}{r^2}$.
$(a)$ If the mass of one object is doubled $(m_1' = 2m_1)$,the new force $F' = \frac{G(2m_1)m_2}{r^2} = 2F$. Thus,the force doubles.
$(b)$ If the distance between the objects is doubled $(r' = 2r)$,the new force $F' = \frac{G m_1 m_2}{(2r)^2} = \frac{G m_1 m_2}{4r^2} = \frac{1}{4}F$. Thus,the force becomes one-fourth of the original force.
$(c)$ If the masses of both objects are doubled ($m_1' = 2m_1$ and $m_2' = 2m_2$),the new force $F' = \frac{G(2m_1)(2m_2)}{r^2} = 4 \times \frac{G m_1 m_2}{r^2} = 4F$. Thus,the force becomes four times the original force.