Determine the volume contraction of a solid copper cube, 10 cm on… - Vidyadip

Question

Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of $7.0 \times 10^6 Pa$.

✓

Answer

Given : $L =10 cm=10 \times 10^{-2} m$
From table,
$
\begin{aligned}
K & =\text { Bulk modulus of elasticity of copper } \\
& =140 \times 10^9 Pa \\
P & =7 \times 10^6 Pa \\
\Delta V & =\text { Volume contraction in a solid copper cube } \\
V & =L \times L \times L=L^3=\left(10 \times 10^{-2}\right)^3 \\
& =1000 \times 10^{-6}=10^{-3} m^3=0.001 m^3
\end{aligned}
$
$K=-\frac{\Delta P}{\frac{\Delta V}{V}}=-\frac{\Delta P V}{\Delta V}$
$
\because \quad \begin{aligned}
\Delta V & =-\frac{\Delta PV}{K}=-\frac{7 \times 10^6 \times .001}{140 \times 10^9} m^3 \\
& =-0.05 \times 10^{-6} m^3=-0.05 cm^3
\end{aligned}
$
Here, negative sign indicates volume contraction.

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