Q: A vessel contains oil (density=0.8 g/cm^{3}) over mercury (density=13.6 g/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 g/cm^{3} is

(a) 3.3

(b) 6.4

(c)7.2

(d) 12.8

Ans: (c)

Sol: Let ρ = density of material of sphere

Applying Law of Floatation ,

Weight = Upthrust

$\large V \rho g = \frac{V}{2} \rho_o g + \frac{V}{2} \rho_m g $

$\large \rho = \frac{\rho_o}{2} + \frac{\rho_m}{2}$

$\large \rho = \frac{0.8}{2} + \frac{13.6}{2}$

= 7.2 g/cm^{3}