The increase in pressure required to decrease the volume of a water sample by 0.2% is P × 10⁵$P \times 10^{5}$ Nm ⁻²$^{-2}$ . Bulk modulus of water is 2.15 × 10⁹$2.15 \times 10^{9}$ Nm ⁻²$^{-2}$ . The value of P is ____.

Related Formula

Core Logic

The change in pressure Δ P$\Delta P$ is the hydrostatic pressure at depth h$h$.

Step 2: Calculation

Given values: ρ = 10³ kg/m³$\rho = 10^3\mathrm{\,kg/m^3}$ g = 10 m/s²$g = 10\mathrm{\,m/s^2}$ β = 9 × 10⁸ N/m²$\beta = 9 \times 10^8\mathrm{\,N/m^2}$ (Δ V)/(V) = -0.02% = -(0.02)/(100)$\frac{\Delta V}{V} = -0.02\% = -\frac{0.02}{100}$

Substitute into the equation:

Chapter Mix

Class 11 Physics: Mechanical Properties Of Solids Class 11 Physics: Mechanical Properties Of Fluids