Question

Take, bulk modulus of water $B=2100 \, MPa$ . What increase in pressure is required to decrease the volume of $200$ litres of water by $0.004$ percent?

• A. $210 \, \, \text{kPa}$
• B. $840 \, \, \text{kPa}$
• C. $8400 \, \, \text{kPa}$
• D. $84 \, \, \text{kPa}$

Answer 1

Answer: (D)

Given,
Bulk modulus of water $B=2100 \, MPa$
$=2100\times 10^{6} \, Pa$
We know that,
$\Delta P=B\left(\frac{- \Delta V}{V}\right)$
Here, $\frac{\Delta V}{V}\times 100$
$\frac{\Delta V}{V}=\frac{0.004}{100}$
$\Delta P=2100\times \left(10\right)^{6}\times \left(\frac{0.004}{100}\right)$
$=\frac{2100 \times 10^{6} \times 4}{1000 \times 100}$
$=\frac{8400 \times 10^{6}}{10^{5}}$
$=84000 \, Pa$
$=84 \, kPa$