The volume of the hollow portion of a sphere is `3/4` of the external volume of the sphere. If it floats in a liquid of relative density `3/2`, half of its external volume immersed, the relative density of the material of the solid is :

Options

A. 2
B. 3
C. `2.4`
D. `1.8`

Answer

B

Explanation

Let `R` be external radius of sphere and `r` be radius of `c`.
Given `4/3 pi r^(3) = 3/4(4/3 pi R^(3)) , r^(3) = 3/4 R^(3)`
Further, `4/3 pi (R^(3)-r^(3))rho g = 1/2 xx 4/3 pi R^(3) xx 3/2 rho_(w)xxg`
Using (i) `(rho)/(rho_w) = 3`.