Question

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

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

Answer 1

Answer: (C)

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