A vessel contains oil (density `0.9" g "c c^(-1)`) over mercury (density 13.6 g `c c^(-1)`). A homogenous sphere floates with one-third of its volume immersed in mercury and the rest immersed in oil. The density of the material of the sphere in g `c c^(-1)` is-

Options

A. 3.3
B. 6.4
C. 5.1
D. 12.8

Answer

C

Explanation

For equilibrium, the total upward push will be equal to the downward pull. If V is the volume of the sphere, then we have:
`(V/3) (13.6)g + (2V)/3 (0.9)g = V rho g`
`therefore rho =(13.6 + 1.8)/2 g cm^(-3) = 5.1 g cm^(-3)`