If the distance between two objects is doubled, what happens to the gravitational force between them? The law of gravitation follows the inverse-square law. The gravitational force (F) is directly proportional to the masses of the two objects ($m_1$ and $m_2$) and inversely proportional to the square of the distance (r) between them. $$ F = \frac{Gm_1 m_2}{r^2} $$ $$ F \propto \frac{1}{r^2} $$ $$ \frac{F_1}{F_2} \propto \frac{r_2^2}{r_1^2} $$ $$ \frac{F_1}{F_2} \propto \frac{(2r_1)^2}{r_1^2} $$ $$ \frac{F_1}{F_2} \propto \frac{4r_1^2}{r_1^2} $$ $$ F_2 \propto \frac{F_1}{4} $$ $$ F_2 = k \frac{F_1}{4} $$ Therefore, if the distance between two objects is doubled, the gravitational force between them becomes one-fourth. ## Physical Properties of Materials 1. When a film of soap appears on water during the day, it shows beautiful colors. The reason for this phenomenon is-