A vessel contains oil (density `=0.8gm//cm^3`) over mercury (density `=13.6gm cm^3`). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in `gm//cm^3` is

Options

A. 3.3
B. 6.4
C. 7.2
D. 12.8

Answer

C

Explanation

`F_B = rho_m (V)/(2) g + rho_o (V)/(2) g`
`W = F_B`
`sigma Vg = rho_m (V)/(2) g + rho_o (V)/(2) g`
`sigma = (rho_m + rho_o)/(2) = (13.6 + 0.8)/(2)`
=`(14.4)/(2) = 7.2 g//c c`.
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