Question

if pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake ?(a) 10m(b) 20m(c) 60m(d) 30m

Answer 1

hey here is your answer
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let's

Depth = d
Atmospheric Pressure = P₀ = 10⁵ Pa
Density of water at 4°C (ρ) = 10³ kg/m³

Pressure at half of depth
P = P₀ + (d/2)ρg
P = P₀ + 0.5dρg

Pressure at the bottom 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

option "b" is the correct answer

I think my answer is capable to clear your confusion