A solid cube of side length 20 cm and density 820 kg/m ^3 floats at the interface of two immiscible liquids. The upper liquid has a density of 700 kg/m ^3 and the lower liquid has a density of 1000 kg/m ^3 . If the cube is completely immersed within the two layers, the height of the cube submerged in the lower liquid is:

Step-by-step solution

Let the total height of the cube be H = 20 cm and the height submerged in the lower liquid be x . Since the cube is completely immersed, the height in the upper liquid is (H - x) = (20 - x) . For equilibrium, the total weight of the cube equals the sum of the buoyant forces from both liquids: W = F_ b1 + F_ b2 _c A H g = _u A (20 - x) g + _l A x g Dividing by A g and substituting the given values: 820 20 = 700 (20 - x) + 1000 x 16400 = 14000 - 700x + 1000x 2400 = 300x x = 8 cm . The height of the cube submerged in