Question

Determine the volume contraction of a solid copper cube, $10\, cm$ 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 $(l)=10\,cm =0.1 \,m$
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 $(K)=\frac{p}{\Delta V / V}=\frac{p V}{\Delta V}$
Or $\Delta V =\frac{p V}{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} $
$=5 \times 10^{-8} m ^{3}$