Question

A metal cube of side $1m$ is subjected to a uniform force acting normally on the whole surface of the cube, If the volume changes by $1.5\times {10}^{-5}{m}^2$ and if the pressure is ${10}^6$ Pa, find the bulk modulus of the metal.

• A. $3.90\times {10}^5{N/m}^3$
• B. $5.24\times {10}^5{N/m}^3$
• C. $6.67\times {10}^{10}{N/m}^3$
• D. $7.53\times {10}^{11}{N/m}^3$

Answer 1

Answer: (C)

$6.67\times {10}^{10}{N/m}^3$

$\begin{array}{cc}\Delta V& =1.5\times {10}^{-5}{m}^2\\ P& ={10}^{6}Pa\\ V& =(1m{)}^3=1m^3\text{(given a cube of side}1m)\end{array}$

$\begin{array}{cc}P& =B\frac{\Delta V}{V}\\ \Rightarrow B=\frac{P}{\Delta V/V}=\frac{{10}^6\times 1}{1.5\times {10}^{-5}}& =0.667\times {10}^{11}N/m^2\\ & =6.67\times {10}^{10}N/m^2\\ \therefore \text{Answer is (C)}& \end{array}$