A cubical metal block with an edge of 12 cm floats in mercury such that one-fifth of its height is submerged. Water is then poured until the upper surface of the block is just immersed. Determine the height of the water column that needs to be poured. The specific gravity of mercury is 13.6 .

Step-by-step solution

Let the edge of the cubical block be L = 12 cm and its base area be A = L^2 . Initially, the block floats in mercury with 1 5 of its height submerged. Equating the weight of the block to the buoyant force provided by mercury: L A _b g = ( L 5 ) A _m g _b = _m 5 = 13.6 5 = 2.72 g/cm ^3 When water is poured until the upper surface of the block is just immersed, let the height of the water column be h . The block is now submerged in water by a height h and in mercury by a height (L - h) . Equating the total buoyant fo