Question

A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When a certain amount of an oil poured into the bucket, it is found that the block is just under the oil surface, with half of its volume underwater and half in oil. The density of oil relative to that of water is-

• A. $0.7$
• B. $0.5$
• C. $0.6$
• D. $0.8$

Answer 1

The correct option is C $0.6$

When no oil poured :

$Mg=\left(\frac{4V}{5}\right){\rho }_{w}g$
${\rho }_{b}Vg=\left(\frac{4V}{5}\right){\rho }_{w}g$
${\rho }_b=\frac{4{\rho }_w}{5}$
After pouring oil into the water :

$Mg=F_{b_1}+F_{b_2}$
$\left({\rho }_{b}V\right)g=\left(\frac{V}{2}\right){\rho }_{\text{oil}}g+\left(\frac{V}{2}\right){\rho }_{w}g$
$\Rightarrow {\rho }_{\text{oil}}=\frac{3}{5}{\rho }_{\text{water}}$
$\therefore \frac{{\rho }_{\text{oil}}}{{\rho }_{\text{water}}}=0.6$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.