Question

Two spheres of the same material and same radius ‘r’ are touching each other gravitational force between them is directly proportional to

• A. $r^2$
• B. $r^3$
• C. $r^4$
• D. $r$

Answer 1

The correct option is C $r^4$

Mass of each metal sphere is given by $m=\frac{4}{3}\pi r^3\rho$

The force of attraction between two metal sphere is given by

$F=\frac{Gmm}{{\left(2r\right)}^2}$

$\therefore F=\frac{G\left(\frac{4}{3}\pi r^3\rho \right)\left(\frac{4}{3}\pi r^3\rho \right)}{4r^2}$

$\therefore F=\frac{G\left(\frac{4}{3}\pi \rho \right)\left(\frac{4}{3}\pi \rho \right)}{4}\frac{r^3\times r^3}{r^2}$

$\therefore F=K{r}^4$