Question

The bulk modulus of water is $2.1\times {10}^{9}N/m^2$. The pressure required to increase the density of water by 0.1 % is

• A. $2.1\times {10}^{3}N/m^2$
• B. $2.1\times {10}^{6}N/m^2$
• C. $1.1\times {10}^{3}N/m^2$
• D. $2.1\times {10}^{5}N/m^2$

Answer 1

The correct option is B $2.1\times {10}^{6}N/m^2$

From Hooke's Law,
Bulk Modulus $\left(B\right)=\frac{Stress\left(\sigma \right)}{strain\left(ϵ\right)}$
$B=\frac{\sigma }{ϵ}=\frac{\sigma V}{\Delta V}$
In terms of density,
$B=\frac{\sigma \rho }{\Delta \rho }$
Hence increse in density is given by,
$\sigma =\frac{\Delta \rho B}{\rho }$
$\sigma =\frac{0.1}{100}\times 2.1\times {10}^9$
We get pressure induced due to stress
$\sigma =2.1\times {10}^6\frac{N}{m^2}$