The atmospheric pressure at the surface of a lake of depth h is P 0 . If the pressure at half the depth of the lake is equal to 2 3 of the pressure at the bottom of the lake, then the depth ( h ) of the lake is

Step-by-step solution

The pressure at half the depth = P 0 + h 2 d g The pressure at the bottom = P 0 + h ρ g According to given condition P 0 + h 2 d g = 2 3 ( P 0 + h d g ) ⇒ 3 P 0 + 3 h 2 d g = 2 P 0 + 2 h d g ⇒ h = 2 P 0 d g = 2 × 10 5 10 3 × 10 = 20   m