A cubical block of steel of density 7.8 gloc floats on mercury (density 13.6 g/cc) with its sides vertical. Take the side cube as 10 cm. If water is poured on the mercury surface. what will be the height of water column, when the surface just covers the top of steel block ?
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The height of the water column will be 4.6 cm
Explanation :
side of the block = 10 cm
=> volume of the block = 10³ = 1000 cc
let h be the height of water column above mercury
=> height of mercury = 10 - h
As water is poured up to the top surface of the block, the weight of the block would be balanced by both displaced mercury and water together.
hence,
1000 x 7.8 x g = 100(10-h) x 13.6 x g + 100(h) x 1 x g
=> 7800 = 13600 - 1360h + 100h
=> 1260h = 13600 - 7800 = 5800
=> h = 5800/1260 = 4.6 cm
Hence the height of the water column will be 4.6 cm
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