How much work is done in raising a stone of mass 5 kg with relative density 3 lying at the bed of a lake through a height of 3 m

( ans= 166.6)

relative density is the ratio of density of object to the density of medium. Here medium is water.

RD = density of stone / density of water = 3

stone is three times denser than water.

According to Archimedes principle of floatation, it will sink at the bottom.

But its Apparent weight inside water will be = Actual weight - Buoyant force

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Actual weight = volume of stone x density of stone x g = mg

Buoyant force = Weight of water displaced by the stone = volume of stone x density of water x g

density of water = density of stone / 3

So buoyant force = volume of stone x (1/3 density of stone) x g = 1/3 actual weight of stone = mg/3

Therefore apparent weight of stone in water = mg - mg/3 = 2mg/3

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Work done to raise it throught height h = apparent weight x h

W = 2mgh /3 = 2 x 5 x 10 x 5 / 3 = 500/3 = 166.67 J