Question

Question 3
The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitational force would become

(a) $\frac{F}{4}$
(b) $\frac{F}{2}$
(c) $F$
(d) $2F$

Answer 1

(a) $\frac{F}{4}$

$F=\frac{G{m}_1{m}_2}{R^2}$
since both masses were made half, we can put,

$m_1=\frac{m_1}{2}$

$M_2=\frac{m_2}{2}$

$F_{new}=\frac{G\left(\frac{m_1}{2}\right)\left(\frac{m_2}{2}\right)}{R^2}=\frac{G{m}_1{m}_2}{4R^2}$

Therefore, $F_{new}=\frac{F}{4}$