Question

A body floats in water with its one-third volume above the surface. The same body floats in a liquid with one-third volume immersed. The density of the liquid is:

• A. 9 times more than that of water
• B. 2 times more than that of water
• C. 3 times more than that of water
• D. 1.5 times more than that of water

Answer 1

The correct option is B 2 times more than that of water

Body floats in water with its one-third volume above the surface, so according to law of floatation, we have
weight of the body $=$ upthrust in water
$\Rightarrow W=\left(\frac{2V}{3}\right){\rho }_{w}g$ .....$\left(I\right)$ Since two-third volume is under the water.
And applying the same for the liquid, we have
$\Rightarrow W=\left(\frac{V}{3}\right){\rho }_{l}g$ .....$\left(II\right)$
from $\left(I\right)$ and $\left(I\right)$, we have
$\left(\frac{2V}{3}\right){\rho }_{w}g=\left(\frac{V}{3}\right){\rho }_{l}g$
$\Rightarrow {\rho }_l=2{\rho }_w$