Question

A vessel contains oil (density = 0.8 gm / $c{m}^3$) Over mercury (density = 13.6 gm / $c{m}^3$). 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/$c{m}^3$

• A. 3.3
• B. 6.4
• C. 7.2
• D. 12.8

Answer 1

The correct option is C

7.2

As the sphere floats in the liquid. Therefore its weight will be equal to the upthrust force on it Weight of the sphere = $\frac{4}{3}\pi R^3\rho g$
Upthrust due to oil and mercury= $\frac{2}{3}\pi R^3\times {\sigma }_{oil}g+\frac{2}{3}\pi R^3{\sigma }_{Hg}g.....\left(ii\right)$
Equating (i) and (ii) $\frac{4}{3}\pi R^3\rho g=\frac{2}{3}\pi R^{3}0.8g+\frac{2}{3}\pi R^3\times 13.6g\Rightarrow 2\rho =0.8+13.6=14.4\Rightarrow \rho =7.2$