Question

Two metal spheres of the same material and radius $r$ are in contact with each other. The gravitational force of attraction between the spheres is given by:

• A. $F=K{r}^4$
• B. $F=K/r^3$
• C. $F=K/4r^2$
• D. $F=k{r}^2$

Answer 1

The correct option is A $F=K{r}^4$

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

$F=K{r}^4$