Question

A copper solid cube of $60mm.$ side is subjected to a pressure of $2.5\times {10}^{7}N/m^2$. If the bulk modulus of copper is $1.25\times {10}^{11}N/m^2$ then the change in the volume of the cube will be :

• A. $43.2{mm}^3$
• B. $33.2{mm}^3$
• C. $23.2{mm}^3$
• D. $432{mm}^3$

Answer 1

Answer: (A)

$43.2{mm}^3$

$\begin{array}{c}l=60mm\\ P=2.5\times {10}^{7}N/m^2\\ B=1.25\times {10}^{11}N/m^2\\ \frac{F}{A}=Stress=B\frac{\Delta V}{V}\end{array}$

$\begin{array}{cc}& \Rightarrow 2\cdot 5\times {10}^7=1.25\times {10}^{11}\times \frac{\Delta V}{{(60\times {10}^{-3})}^3}\\ & \Rightarrow \Delta v=\frac{{2\cdot 5\times {10}^7\times (60\times {10}^{-3})}^3}{1.25\times {10}^{11}}\\ \Rightarrow & \Delta v=432\times {10}^{-10}{am}^3\end{array}$

$\begin{array}{c}\Rightarrow \Delta v=432\times {10}^{-1}{mm}^3=43.2{mm}^3\\ \text{Ans : (A)}\end{array}$