Question

Two metal spheres of radius $r$ are kept in contact. If ${}^{\prime }{d}^{\prime }$ is the density of each sphere material, the gravitational force between them is proportional 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 $d^2{r}^4$

Mass of each metallic sphere $=$ Volume $\times$ Density

$\Rightarrow M=\frac{4}{3}\pi r^3\times d$ ( radius $=r$ and density $=d$)

Now the distance between centers of the two spheres is :

$D=2r$

So Gravitational force between them is given by

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

So F is proportional to $d^2{r}^6$