Question

A solid copper cube of $7cm$ edge is subjected to a hydraulic pressure of $8000kPa$. The volume contraction of the copper cube is (Bulk modulus of copper = $140GPa$ )

• A. $196\times 10^{-3}c{m}^3$
• B. $19.6\times 10^{-6}c{m}^3$
• C. $19.6\times 10^{-3}c{m}^3$
• D. $196\times 10^{3}c{m}^3$

Answer 1

Answer: (C)

Given,
edge of solid copper cube, $l=7cm$
hydraulic pressure, $p=8000kPa=8000\times 10^{3}Pa$
and Bulk modulus of copper, $\beta =140GPa$
$=140\times 10^{9}Pa$
As we know that,
Bulk modulus, $\beta =\frac{p}{\left(\frac{\Delta V}{V}\right)}$
or $\beta =\frac{pV}{\Delta V}$
$\therefore \Delta V=\frac{pV}{\beta }=\frac{8000\times 10^3\times (l{)}^3}{140\times 10^9}$
$=\frac{8000\times 10^3\times (7{)}^3}{140\times 10^9}$
$=19.6\times 10^{-3}c{m}^3$