Q. Two spheres of radius $r$ and $2r$ are touching each other. The fore of attraction between them is proportional to
A) $r^{6}$
B) $r^{4}$
C) $r^{2}$
D) $r^{- 2}$
Explanation
(d) $F = \frac{Gm_{1}m_{2}}{(r + 2r)^{2}} = \frac{Gm_{1}m_{2}}{9r^{2}},ie,\ F \propto r^{- 2}$
Note that $F \propto r^{4}$ by taking $m = \frac{4}{3}\pi r^{4}\rho$ and then
$F \propto \frac{r^{3}r^{3}}{r^{2}},ie,\ F \propto r^{4}$
is not correct because the gravitational law obeys inverse square law and is not related with densities
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.