Question

Two metal spheres each of radius 'r' are kept in contact with each other. If d is the density of the material of the sphere, then the gravitational force between those spheres is propositional to

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

Answer 1

The correct option is B $d^2{r}^4$

the mass of each sphere is given by:

$M=volume\times density=\frac{4}{3}\pi r^2\times d$

now distance between the centers of the two spheres $=2r$ so gravitational force between them $\left(F\right)=\frac{GMM}{(2r{)}^2}$

$\Rightarrow F=\frac{16G{\pi }^2}{9\times 4}\frac{d^2{r}^6}{r^2}$

So $F$ is directly proportional to $d^2{r}^4$