Question

A body floats in water with $40\%$ of its volume outside water. When this body is kept in oil, it floats with $60\%$ of its volume remains outside the oil. The relative density of oil is $\frac{K}{2}$. Find value of $K$.

Answer 1

let $\rho$ be density of water be ${\rho }_0$

It submerged $60\%$ o water and $40\%$ in oil .

Let the body density be $\rho$.

$\rho vg={\rho }_{0}v\times 0.6\times g\to \left(1\right)$

$\rho vg={\rho }_{oil}v\times 0.4\times g\to \left(2\right)$

Divide $\left(2\right)$ by $\left(1\right)$

$\frac{{\rho }_{oil}}{{\rho }_0}\times \frac{4}{6}=1$

$\frac{k}{2}=\frac{3}{2}$

$k=3$