The density of the wood and the oil is 615 kg/m^3 and 690kg/m^3 .
(a) Finding the density of wood ([tex]$\rho_{\text {wood }}$[/tex])
Taking the density of water as [tex]$\rho_{\text {water }}=1000 \mathrm{~kg} / \mathrm{m}^3$[/tex]
Based on the principle of floatation:
- fraction of volume submerged in water = Ratio of density of wood to the density of water
-[tex]$f_w=\frac{\rho_{\text {wood }}}{\rho_{\text {water }}}$[/tex]
-[tex]0.615=\frac{\rho_{\text {wood }}}{1000 \mathrm{~kg} / \mathrm{m}^3}[/tex]
- [tex]$\rho_{\text {wood }}=615 \mathrm{~kg} / \mathrm{m}^3$[/tex]
(b) Finding the density of oil ( [tex]$\rho_{\text {oil }}$[/tex] )
Similar to (a),
- fraction of volume submerged in oil = Ratio of density of wood to the density of oil
- [tex]$f_o=\frac{\rho_{\text {wood }}}{\rho_{\text {oil }}}$[/tex]
- [tex]$0.892=\frac{615 \mathrm{~kg} / \mathrm{m}^3}{\rho_{\text {oil }}}$[/tex]
- [tex]$\rho_{\text {oil }} \approx 690 \mathrm{~kg} / \mathrm{m}^3$[/tex]
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