A hemispherical bowl just floats without sinking in a liquid of density `1.2xx10^(3)kg//m^(3)`. If outer diameter and the density of the bowl are `1m` and `2 xx 10^(4) kg//m^(3)` respectively, then the inner diameter of bowl will be

Options

A. `0.94m`
B. `0.97m`
C. `0.98m`
D. `0.99m`

Answer

C

Explanation

Let `d` be the inner diameter of the hemispherical bowl. Then
`B=mg`
`4/3pixx(1/2)^(3)xx(1.2xx10^(3))g=4/3pi[(1/2)^(3)-(d/2)^(3)]xx(2xx10^(4))g`
Solving we get `d=0.98m`