Question

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.

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Answer

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,

{Volume\ of\ immersed\ part\over Total\ volume} = {Density\ of\ wood\over Density\ of\ water}

{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,

{Volume\ of\ immersed\ part\over Total\ volume} = {Density\ of\ wood\over Density\ of\ oil}

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

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

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