Question

A vessel contains oil (density = 0.8 gm/cm³) over mercury (density = 13.6 gm/cm³). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm³ is

• A. (a) 3.3
• A. (b) 6.4
• A. (c) 7.2
• A. (d) 12.8

Answer 1

(c)

As the sphere floats in the liquid. Therefore its weight will be

equal to the upthrust force on it

Weight of sphere $= \frac { 4 } { 3 } \pi R ^ { 3 } \rho g$ .... (i)

Upthrust due to oil and mercury

......(ii)

Equating (i) and (ii)

$\Rightarrow 2 \rho = 0.8 + 13.6 = 14.4 \Rightarrow \rho = 7.2$