A wooden block floats in water with two-third of it’s volume submerged. (a) Calculate the density of wood. (b) When the same block is placed in oil, three-quarter of it’s volume is immersed in oil. Calculate the density of oil.

Let volume of wooden block be V.

Volume of block submerged in water = 2\over 3V

Density of water = 1000 kg m^-3

By the principle of floatation,

⇒ {2V/3\over V} = {Density\ of\ wood\over Density\ of\ water}

∴ Density of wood = {2\over 3}×1000 = 667 kg m^-3

(b) Volume of block submerged in oil = {3\over 4}V

By the principle of floatation,

⇒ {3V/4\over V} = {667\over Density\ of\ oil}

⇒ Density of oil = 4\over 3 × 667 = 889.33 kg m^-3