Question

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

• A. $ 2\times 10^{9}N/m^{2}$
• B. $2 \times 10^{8} N / m ^{2}$
• C. $2 \times 10^{6} N / m ^{2}$
• D. $2 \times 10^{4} N / m ^{2}$

Answer 1

The Correct Option is C

Mass $=$ Volume $\times$ density $=V d=$ constant $V \Delta d +d \Delta V=0$ $\frac{\Delta V}{V} =-\frac{\Delta d}{d}$ $=-\frac{0.1}{100}=10^{-3}$ Bulk modulus $K=-\frac{\Delta p}{\Delta V / V}$ $\Delta p =-K \frac{\Delta V}{V}$ $\Delta p =2 \times 10^{9} \times 10^{-3}$ $=2 \times 10^{6} N / m ^{2}$