Q. 185.0( 1 Vote )

A cubical metal block of edge 12 cm floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is just immersed in it. Find the height of the water column to be poured. Specific gravity of mercury = 13.6.

Answer :

The edge of the block,

Volume of the block,


Volume immersed in mercury,


Now, the buoyant force on the block is equal to the weight of the mercury displaced —————(1)


Let the water be poured to a height “h”.


The buoyant force on the block due to water is equal the sum of the weight of the water displaced and the weight of the mercury displaced.


Volume of block in water,


Volume of block in mercury,


Therefore, the buoyant force is equal to, —————(2)


The buoyant force is equal to the weight of the cube. Therefore, equating (1) and (2),



Solving for h, we get



(ANS)


So the water needs to be poured to a height of 10.4 cm.


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