The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth 'h' of the lake is ( = density of water in the lake, g = acceleration due to gravity, P₀ = atmospheric pressure).

Step-by-step solution

Let the depth of the lake be h . Pressure at half the depth of the lake is given by P₁ = P₀ + g h 2 . Pressure at the bottom of the lake is given by P₂ = P₀ + g h . According to the given condition, P₁ = 2 3 P₂ . Substituting the expressions for P₁ and P₂ : P₀ + g h 2 = 2 3 (P₀ + g h) P₀ - 2 3 P₀ = 2 3 g h - 1 2 g h P₀ 3 = g h 6 h = 2P₀ g Answer: 2P₀ g