A body P floats in water with half its volume immersed. Another body Q floats in a liquid of density 3 4 t h of the density of water with two-third of the volume immersed. The ratio of density of P to that of Q is

Step-by-step solution

Let, for body P , volume = V P Given, Immersed volume = V P 2 For body Q volume = V Q Immersed volume = 2 3 V Q According to Archimedes principle, ∵ Weight of body = weight of fluid displaced For body P , V p ρ p g = 1 2 V p ρ ω g So, ρ P ρ w = 1 2 .....(i) For body Q , V Q ρ Q g = 2 3 V Q 3 4 ρ w g ∵ d e n s i t y o f l i q u i d = 3 4 ρ w So, ρ Q ρ w = 1 2 .....(ii) From Equations (i) and (ii), ρ P ρ Q = 1 or ρ P : ρ Q = 1 : 1