Question:
The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitation force would become
(a) $F / 4$
(b) $F / 2$
(c) $F$
(d) $2 \mathrm{~F}$
Solution:
(a) $\mathrm{F}=\frac{\mathrm{G} m_{1} m_{2}}{r^{2}}, \mathrm{~F}^{\prime}=\frac{\mathrm{G}\left(m_{1} / 2\right)\left(m_{2} / 2\right)}{r^{2}}=\frac{\mathrm{F}}{4} .$