Bulk modulus of water is $2 \times 10^9 \mathrm{~N} / \mathrm{m}^2$. The pressure required to increase the…

Bulk modulus of water is $2 \times 10^9 \mathrm{~N} / \mathrm{m}^2$. The pressure required to increase the volume of water by $0.1 \%$ in $\mathrm{N} / \mathrm{m}^2$ is :
  1. $2 \times 10^9$
  2. $2 \times 10^0$
  3. $2 \times 10^6$
  4. $2 \times 10^4$

Solution

Bulk modulus, $K=2 \times 10^9 \mathrm{~N} / \mathrm{m}^2$ Change in volume, $\Delta V=0.1 \%$ of initial volume $=0.1 \%$ of $V=\frac{V \times 0.1}{100}=V \times 10^{-3}$ $\therefore \quad K=\frac{p V}{\Delta V}$ $2 \times 10^9=\frac{p \times V}{V \times 10^{-3}}$ $p=2 \times 10^9 \times 10^{-3}$ $=2 \times 10^6 \mathrm{~N} / \mathrm{m}^2$

Asked in: AP EAMCET 2003

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