Answer
The density of the oil is $0.74~g/cm^3$
Work Step by Step
If the wood is floating in the oil, then the buoyant force is equal in magnitude to the weight of the wood. According to Archimedes' principle, the buoyant force is equal to the weight of the oil that is displaced.
Let $V$ be the volume of the wood. Let $m_w$ be the mass of the wood. Let $m_o$ be the mass of the oil that is displaced by the wood.
We can find the density of the oil $\rho_o$:
$m_o~g = m_w~g$
$m_o = m_w$
$\rho_o~(0.900~V) = \rho_w~V$
$\rho_o = \frac{\rho_w}{0.900}$
$\rho_o = \frac{0.67~g/cm^3)}{0.900}$
$\rho_o = 0.74~g/cm^3$
The density of the oil is $0.74~g/cm^3$.
