Question

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

• A. $5\times 10^{-2}c{m}^3$
• B. $10\times 10^{-2}$ $c{m}^3$
• C. $15\times 10^{-2}$ $c{m}^3$
• D. $20\times 10^{-2}$ $c{m}^3$

Answer 1

Answer: (A)

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