Question

A vessel contains oil $(\rho =0.8gm/c{m}^3)$ over mercury $(\rho =13.6gm/c{m}^3)$. A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. Then density of material of the sphere in $gm/c{m}^3$ is

• A. 3.3
• B. 6.4
• C. 7.2
• D. 2.8

Answer 1

The correct option is C 7.2

Half of sphere immersed in mercury and half in oil.
Thus there will be upthrust due to both liquids.
Lets ${\rho }_d$ be the density of sphere
Upthrust due to buoyancy = Mass of mercury displaced + mass of oil displaced
Upthrust =$\frac{v}{2}\times 13.6\times g+\frac{v}{2}\times 0.8\times g$
Downward gravitational force due to sphere = $v\times {\rho }_d\times g$
Downward gravitational force = Upthrust due to buoyancy
$v\times {\rho }_d\times g$=$\frac{v}{2}\times 13.6\times g+\frac{v}{2}\times 0.8\times g$
${\rho }_d=7.2gm/c{m}^3$