Question

A wooden cube of side 10 cm has mass 700 g. What part of it remains above the water surface while floating vertically on the water surface?

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Answer

Volume of wooden cube = 10 cm × 10 cm × 10 cm = 1000 cm3

Mass = 700 g

Density = Mass/ volume = 700/1000 = 0.7 g cm-3

By the principle of floatation,

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

Density of water = 1 g cm-3

Density of wooden cube = 0.7 g cm-3

{Volume\ of\ immersed\ part\over Total\ volume}={0.7\over 1}

Hence, fraction submerged = 0.7

Height of wooden cube = 10 cm

Part of woden cube which is submerged = 10 x 0.7 = 7 cm

Therefore, part above water = 10 – 7 = 3 cm

Hence, 3 cm of height of the wooden cube remains above water while floating.

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