Question

Determine the volume contraction of a solid copper cube, $10cm$ on an edge, when subjected to a hydraulic pressure of $7\times 10^6$ Pa. $K$ for copper $=140\times 10^{9}Pa$.

• A. $5\times 10^{-7}{m}^3$
• B. $4\times 10^{-8}{m}^3$
• C. $5\times 10^{-8}{m}^3$
• D. $6\times 10^{-8}{m}^3$

Answer 1

Answer: (C)

Given, each side of cube $(l)=10cm=0.1m$
Hydraulic pressure $(p)=7\times 10^{6}Pa$
Bulk modulus for copper $(K)=140\times 10^{9}Pa$
Volume contraction $(\Delta V)=?$
Volume of the cube $(V)=l^3=(0.1{)}^3=1\times 10^{-3}{m}^3$
Bulk modulus for copper $(K)=\frac{p}{\Delta V/V}=\frac{pV}{\Delta V}$
Or $\Delta V=\frac{pV}{K}$
$\Delta V=\frac{7\times 10^6\times 1\times 10^{-3}}{140\times 10^9}$
$=\frac{1}{20}\times 10^{-6}{m}^3$
$=0.05\times 10^{-6}{m}^3$
$=5\times 10^{-8}{m}^3$