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

Options

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

Answer

c

Explanation

Let density of sphere is `rho` ,
Density of oil is `rho_(1)` and density of mercury is `rho_(2)` Weight of sphere `W=(4)/(3)piR^(3)rhog` ….(1)
Where R= radius of sphere
Buoyant force on sphere in oil ,
`F_(1)=(2)/(3)piR^(3)rho_(1)g` ....(2)
Buoyant force on sphere in mercury,
`F_(2)=(2)/(3)piR^(2)rho_(2)g`....(3)
Weight of sphere `W=F_(1)+F_(2)`
`therefore(4)/(3)piR^(3)rhog=(2)/(3)piR^(3)rho_(1)g+(2)/(3)piR^(3)rho_(2)g`
`therefore2rho=rho_(1)+rho_(2)`
`therefore2rho=0.8+13.6`
`therefore2rho=14.4`
`thereforerho=7.2gcm^(-3)`