Question

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

Answer 1

The height of water column will be 10.37 cm

Explanation :

We know that for floating objects,

weight of the block = weight of the mercury displaced

=> mg = m'g

=> ρALg = ρ'ALg/5

=> ρ = ρ'/5 = 13.6/5 = 2.72

Now in the second case water is filled in the rest of the space,

let the height of the block immersed in mercury = x

=> height of the block immersed in water = 12 - x

hence

weight of block = weight of mercury displaced + weight of water displaced

=> 2.72 x A x 12 x g = 13.6 x A x(X) x g + 1 x A x (12-x) x g

cancelling Ag from both sides

=> 32.64 = 13.6x + 12-x

=> 12.6x = 20.64

=> x = 20.64/12.6 = 1.63

hence height of water column = 12 - x = 12 - 1.63 = 10.37 cm