Question

The density of liquid remains unchanged at various position . now,if the pressure at half depth is 3/5 times the pressure at its bottom then the depth of the lake

Answer 1

Profundity = d, Atmospheric Pressure = P₀ = 10⁵ Pa,

Density of water at 4°C (ρ) = 10³ kg/m³, Pressure at half of profundity, P = P₀ + (d/2)ρg, P = P₀ + 0.5dρg.

Weight at the base of lake P' = P₀ + dρg.

Given that P = 2P'/3, P₀ + 0.5dρg = 2(P₀ + dρg)/3, P₀ + 0.5dg = 2P₀/3 + 2dρg/3, P₀/3 = dρg/6, d = 2P₀/(ρg), d = (2 × 10⁵ Pa)/(10³ kg/m³ × 10 m/s²),d = 20 m, Depth of lake is 20 m