Question

A brass rod has length $0.2m$, area of cross section $1.0$ and Young's modulus ${10}^{11}N{m}^{-2}$. If it is compressed by $5.wt$ along its length, then the change in its energy will be ?

• A. An increase of $2.4\times {10}^{-5}J$
• B. An decrease of $2.4\times {10}^{-5}J$
• C. An increase of $2.4\times {10}^{7}J$
• D. An decrease of $2.4\times {10}^{7}J$

Answer 1

Answer: (A)

An increase of $2.4\times {10}^{-5}J$

$\begin{array}{c}l=0.2m\\ A=0.1{cm}^2\\ Y={10}^{11}N/m^2\\ F=5\times g\\ \Delta l=\frac{F/A}{Y/L}\end{array}$

$\begin{array}{cc}& \\ \Rightarrow \Delta l=\frac{5\times 9.8\times 0.2}{1\times {10}^{-4}\times {10}^{11}}=9.8\times {10}^{-7}m& \\ \text{Energy,}E& =\frac{1}{2}\times F\times \Delta l\\ & =\frac{1}{2}\times 5\times 9.8\times 9.8\times {10}^{-7}\\ & =240.1\times {10}^{-7}\\ & =2.401\times {10}^{-5}Joules\end{array}$

$\begin{array}{c}\text{Since the rod is compressed, Energy will increase.}\\ Ans:\text{(A)}\end{array}$