A liquid is compressed in a cylinder from a volume of 0.02 m3 at 200 N/m2 pressure to a volume of 0.01 m3 at 400 N/m2 pressure. The bulk modulus of el

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A liquid is compressed in a cylinder from a volume of 0.02 m3 at 200 N/m2 pressure to a volume of 0.01 m3 at 400 N/m2 pressure. The bulk modulus of elasticity of the liquid is

1. 500 N/m2
2. 1000 N/m2
3. 400 N/m2
4. 600 N/m2

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Correct Answer - Option 3 : 400 N/m2

Concept:

The bulk modulus of elasticity of the liquid is given by

$K = - \frac{{{{\Delta }}P}}{{\left( {\frac{{{{\Delta }}V}}{V}} \right)}}\;$

Calculation:

Given:
V1 = 0.02 m3, P1 = 200 , V2 = 0.01 m3, P2 =  400 N/m2

$K = - \frac{{{{\Delta }}P}}{{\left( {\frac{{{{\Delta }}V}}{V}} \right)}}\ =- \frac{P_2-P_1}{\frac{V_2-V_1}{V_1}}=-\frac{400-200}{\frac{0.01-0.02}{0.02}}= 400\; N/m^2$

The bulk modulus of elasticity of the liquid is 400 N/m2.

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