A block of wood floats in water with (4 / 5) th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is (in kgm ⁻³ )

Step-by-step solution

Let V be the volume of the block and _ w be the density of water. Let _ b be the density of the block and _ l be the density of the liquid. When the block floats in water, the weight of the block equals the weight of the displaced water: _ b V g = _ w V_ sub g Given V_ sub = 4 5 V , we have: _ b V g = _ w ( 4 5 V ) g _ b = 4 5 _ w Taking the density of water _ w = 1000 kg/m ³ , we get _ b = 4 5 1000 = 800 kg/m ³ . When the block just floats in the liquid, the entire volume of the block is submerged, so the weight o