Question

The volume change of a solid copper cube $10 \,cm$ on an edge, when subjected to a pressure of $7 \,MPa$ is
(Bulk modulus of copper =$140\, GPa$)

• A. $5\times10^{-2} cm^{3}$
• B. $10\times10^{-2}$ $cm^{3}$
• C. $15\times10^{-2}$ $cm^{3}$
• D. $20\times10^{-2}$ $cm^{3}$

Answer 1

Answer: (A)

Here, $L=10\, cm=10\times10^{-2}\,m$
$p=7\, Mpa$ $=7\times10^{6} pa$
$B=140 Gpa$ $=140\times10^{9} \,pa$
As $B=\frac{P}{\Delta V /V}$
$\therefore \quad$ $\Delta V$ $=\frac{PV}{B}$ $=\frac{PL^{3}}{B}$ $=\frac{\left(7\times10^{6}pa\right)\left(10\times10^{-2}m\right)^{3}}{140\times10^{9}pa}$
$=5\times10^{-8}m^{3}=5\times10^{-2} cm^{3}$