A block of wood floats in water with two third of its volume submerged. In oil, the block floats with $0.90$ of its volume submerged. The densities of (a) wood and (b) oil are [Density of water is ${10}^{3}kg/m^3$]

The correct option is B $667kg/m^3$, $740kg/m^3$

Let in water,

volume of wood be $v$, for equilibrium,

density of wood $=d$

Density of oil$=D$

weight of wood=upthrust from water$\Rightarrow vd=\frac{2v}{d}\times 1000$

$\Rightarrow d=\frac{2}{3}\times 1000kg/m^3=667kg/m^3$

In oil,

for equilibrium,

$v\times d={10}^3\times 0.9v\times D$

$\Rightarrow d=0.9D$

$\Rightarrow \frac{2}{3}\times \frac{1000}{0.9}=D$

$\Rightarrow D=740kg/m^3$