Question

The bulk modulus of water is $2.0\times {10}^{9}N/m^2$ The pressure required to increase the density of water by $0.1\%$ is :

• A. $2.0\times {10}^{3}N/m^2$
• B. $2.0\times {10}^{6}N/m^2$
• C. $2.0\times {10}^{5}N/m^2$
• D. $2.0\times {10}^{7}N/m^2$

Answer 1

The correct option is B $2.0\times {10}^{6}N/m^2$

${\rho }^{{}^{\prime }}=\rho (1+\frac{dp}{B})$

change in density $\Delta \rho ={\rho }^{{}^{\prime }}-\rho =\frac{\rho dp}{B}$

$\frac{\Delta \rho }{\rho }=\frac{dp}{B}$

$\frac{\Delta \rho }{\rho }\times 100=0.1$

$\frac{\Delta \rho }{\rho }=0.001$

$\Delta P=B\frac{\Delta \rho }{\rho }=2\times {10}^9\times 0.001=2\times {10}^{6}N/m^2$