Question

How much should the pressure on a litre of water be changed to compress it by $0.10\%$. Bulk modulus of water $=2.2\times {10}^9{\text{Nm}}^{-2}$

• A. $2.2\times {10}^6{\text{N/m}}^2$
• B. $2.2\times {10}^9{\text{N/m}}^2$
• C. $24\times {10}^4{\text{N/m}}^2$
• D. $32\times {10}^4{\text{N/m}}^2$

Answer 1

The correct option is A $2.2\times {10}^6{\text{N/m}}^2$

Here, Volume of water, $V=1\text{L}$

Change in volume upon compression,$\Delta V=-0.10\%$ of $V$

$=-\frac{0.10}{100}\times 1$

$=-\frac{1}{1000}\text{L}$

Let $\Delta p=$ change in pressure required for compression of $1\text{L}$ of water

$B=$ bulk modulus of water $=2.2\times {10}^9{\text{Nm}}^{-2}$

Using the realation $B=\frac{-\Delta p}{\frac{\Delta V}{V}}$ , we get

$\Delta p=-B\frac{\Delta V}{V}$

$=2.2\times {10}^9\times \frac{{10}^{-3}}{1}$

$\therefore \Delta p=2.2\times {10}^6{\text{Nm}}^{-2}$

Hence, option $\left(\text{A}\right)$ is correct.