Question

A lake has a depth of 500m. The bulk modulus of water is 2*10^9N/m^2. Calculate the fractional compression, ΔV/V, of water at the bottom of the lake.

(a) 2.5*10^-3

(b) 7*10^-3

(c) 3.5*10^-3

(d) 5*10^-3

I had been asked this question in semester exam.

The origin of the question is Solids Mechanical Properties in division Mechanical Properties of Solids of Physics – Class 11

Answer 1

Correct option is (a) 2.5*10^-3

For explanation I would say: Pressure at the bottom ‘P’ = ρgh = 1000*10*500 = 5*10^6Pa.

B = -P/(ΔV/V)

∴ ΔV/V = -P/B = 5*10^6/2*10^9 = 2.5*10^-3.