Question

 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

Answer 1

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.