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A liquid compressed in a cylinder has a volume of 0.04 m3 at 100 kg/cm2 and a volume of 0.039 m3 at 200 kg/cm2. The bulk modulus of elasticity of liquid is
1. 4000 kg/cm2
2. 400 kg/cm2
3. 40 × 105 kg/cm2
4. 40 × 106 kg/cm2

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Correct Answer - Option 1 : 4000 kg/cm2

Concept:

Bulk modulus (K) \( = \frac{{ - {\rm{\Delta }}P}}{{\left( {\frac{{{\rm{\Delta }}V}}{V}} \right)}}\)

Where, ΔV = change in volume = V2 – V1, ΔP = change in pressure = P2 – P1

Calculation:

Given:

V1 = 0.04 m3 = 40000 cm3, V2 = 0.039 m3 = 39000 cm3, P1 = 100 kg/cm2, P2 = 200 kg/cm2, K = ?

ΔV = V2 – V1 = 39000 - 40000 = -10000 cm3,

ΔP = P2 – P1 = 100 kg/cm2.

Bulk modulus (K) \( = \frac{{ - {\rm{\Delta }}P}}{{\left( {\frac{{{\rm{\Delta }}V}}{V}} \right)}}\)

\(= \frac{{ - \left( {200 - 100} \right)}}{{\frac{{\left( {39000 - 40000} \right)}}{{40000}}}}\)

K = 4000 kg/cm2

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