Question

Two metal spheres of equal radius r are touching each other. The force of attraction F between them is

• A. $F\propto r^4$
• B. $F\propto r^6$
• C. $F\propto r^2$
• D. $F\propto \frac{1}{r^2}$

Answer 1

The correct option is A $F\propto r^4$

F = $\frac{G{M}^2}{4R^2}$

Density is defined as mass upon volume i.e density = $\frac{mass}{volume}$

Mass = density $\ast$ volume

M = density $\ast$ $\frac{4\pi R^3}{3^{}}$

Squaring on both sides,

M${}^2$ = density${}^2$ $\ast$ ($\frac{4\pi }{3}$)${}^2$ $\ast$ R${}^6$

Here F = G. (density${}^2$) ($\frac{4\pi }{3}$)${}^2$ $\ast$ R

Therefore F is directly proportional to r${}^4$