Question

When the pressure of the liquid is increased from 3 MN/m² to 6 MN/m², its volume is decreased by 0.1%. The bulk modulus of elasticity of the liquid will be
1. 3 × 10¹² N/m² 
2. 3 × 10⁹ N/m²
3. 3 × 10⁸ N/m²
4. 3 × 10⁴ N/m²

Answer 1

Correct Answer - Option 2 : 3 × 10⁹ N/m²

Concept:

The bulk modulus of elasticity of the liquid is given by

\(\rm K = - \dfrac{{{{Δ }}P}}{{\left( {\dfrac{{{{Δ }}V}}{V}} \right)}}\;\)  

Calculation:

Given:

P₁ = 3 MN/m², P₂ = 6 MN/m², and ΔV = 0.1%

ΔP = P₂ - P₁ = 6 – 3 = 3 MN/m², \(\rm {Δ V\over V}=-0.001\)

\(\rm K = - \dfrac{{3 \times {{10}^6}}}{{ - 0.001}} = 3 \times {10^9}\;N/{m^2}\)