Question

The compressibility of water is $5\times {10}^{-10}{m}^2/N$ and subjected to a pressure of 15 MPa.The fractional decrease in volume will be

• A. $7.5\times {10}^{-3}$
• B. $5\times {10}^{-3}$
• C. $2.5\times {10}^{-3}$
• D. $1.25\times {10}^{-3}$

Answer 1

The correct option is A $7.5\times {10}^{-3}$

$\begin{array}{c}\text{Compressibily}\left(\gamma \right)=\frac{1}{\text{Bulk Modulus}\left(B\right)}=5\times {10}^{-10}\\ P=15MPa\\ \text{We know ,}\\ P=-B\frac{\Delta V}{V}\end{array}$

$\begin{array}{cc}& \begin{array}{cc}\Rightarrow \frac{\Delta V}{V}=-\frac{P}{B}=-15\times {10}^6\times 5\times {10}^{-10}& =-75\times {10}^{-4}\\ & =-7.5\times {10}^{-3}\end{array}\\ & \text{Answer:}\left(A\right)\end{array}$