Q. Two balls, each of radius $R$, equal mass and density are placed in contact, then the force of gravitation between them is proportional to
A) $F \propto \frac{1}{R^{2}}$
B) $F \propto R$
C) $F \propto R^{4}$
D) $F \propto \frac{1}{R}$
Explanation
(c) [image:8_image54.emf]
Let masses of two balls are $m_{1} = m_{2} = m$ (given) and the density be $\rho$.
Distance between their centres$\ = AB = 2R$
Thus, the magnitude of the gravitational force F that two balls separated by a distance 2R exert on each other is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ F = G\frac{(m)(m)}{(2R)^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = G\frac{m^{2}}{{4R}^{2}} = G\frac{\left( \frac{4}{3}\pi R^{3}\rho \right)^{2}}{{4R}^{2}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ F \propto R^{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.