Question

A spherical ball of volume $1000c{m}^3$ is subjected to a pressure of $10$ atmosphere. The change in volume is ${10}^{-2}c{m}^3$. If the ball is made of iron find its bulk modulus.

• A. $1\times {10}^{11}N/m^2$
• B. $2\times {10}^{11}N/m^2$
• C. $3\times {10}^{11}N/m^2$
• D. $4\times {10}^{11}N/m^2$

Answer 1

The correct option is A $1\times {10}^{11}N/m^2$

$\begin{array}{cc}\text{Given pressure}& =10\text{atm}\\ & =10\times {10}^{5}Pa\\ \text{volume}& ={10}^3\times {\left({10}^{-2}\right)}^3{m}^3\\ & ={10}^{-3}{m}^3\end{array}$

$\begin{array}{cc}\text{change in volume}& ={10}^{-2}{cm}^3\\ & ={10}^{-2}\times {10}^{-6}{m}^3\\ & ={10}^{-8}{m}^3\\ B=\frac{pv}{\Delta v}& =\frac{10\times {10}^5\times {10}^{-3}}{{10}^{-8}}\\ B& ={10}^{11}N/m^2\end{array}$