A hollow metallic sphere with internal and external radii r₁ and r₂ respectively floats on the surface of liquid. The density of liquid is ${\mathrm{\rho }}_1$ and density of material of sphere is ${\mathrm{\rho }}_2$.
What fraction of the sphere is inside the liquid?

• A

  $\left(1-\frac{{\mathrm{r}}_1^3}{{\mathrm{r}}_2^3}\right)\frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1}$

• B

  $\left(1-\frac{{\mathrm{r}}_1^3}{{\mathrm{r}}_2^3}\right)\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2}$

• C

  $\left(1+\frac{{\mathrm{r}}_1^3}{{\mathrm{r}}_2^3}\right)\frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1}$

• D

  $\left(1+\frac{{\mathrm{r}}_2^3}{{\mathrm{r}}_1^3}\right)\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2}$