A wooden block floats with 3 5 of its volume submerged in a tank of water. If a denser liquid is poured into the tank, the wooden block floats with half its volume in the liquid and the remaining half in water. The relative density of the liquid is:

Step-by-step solution

Let V be the volume of the wooden block and _ w be the density of water. Let _ b be the density of the block and _ l be the density of the denser liquid. In the first case, the block floats in water. By the principle of flotation, the weight of the block equals the weight of the displaced water: _ b V g = _ w ( 3 5 V) g _ b = 3 5 _ w In the second case, the block floats in a mixture of water and the denser liquid. The total buoyant force equals the weight of the block. The block has half its volume in the liquid an