A cubical metal block of edge 12 cm floats in mercury with o

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.

Solution

Given, x = 12 cm Length of the edge of the block Hg= 13.6 gm/cc Given that, initially 1/5 of block is inside mercuty. Let bdensity of block in gm/cc. (x)3 * b * g = (x)2 * (x/5) * Hg * g 123 * b = 122 * 12/5 * 13.6 b = 13.6/5 gm/cc After water poured, let x = height of water column. Vb= VHg + Vw= 123 Where VHg and Vw are volume of block inside mercury and water respectively (Vb * b * g) = (VHg * Hg * g) + (Vw * w * g) (VHg + Vw)b = VHg * Hg + Vw * w. (VHg + Vw) × 13.6/5 VHg * 13.6 + Vw * 1 (12)3 * 13.6/5 = (12 – x) * (12)2 * 13.6 + (x) * (12)^2 * 1 x = 10.4 cm