Question

A wire of length $L_0$ is supplied heat to raise its temperature by $T.$ if $\gamma$ is the coefficient of volume expansion of the wire and $Y$ is Young's modulus of the wire then the energy density stored in the wire is

• A. $\frac{1}{2}{\gamma }^2{T}^2{Y}^{-1}$
• B. $\frac{1}{3}{\gamma }^2{T}^2{Y}^3$
• C. $\frac{1}{18}\frac{{\gamma }^2{T}^2}{Y}$
• D. $\frac{1}{18}{\gamma }^2{T}^{2}Y$

Answer 1

The correct option is A $\frac{1}{2}{\gamma }^2{T}^2{Y}^{-1}$

$\begin{array}{c}u=\frac{1}{2}\left(Y\right)\times {\left(strain\right)}^2\\ \Delta T=T\\ \gamma =\frac{\Delta V}{V\Delta T}=\frac{\Delta V}{VT}\\ strian=\frac{\Delta V}{V}=\gamma T\\ substutaingthevalueinequation\left(1\right)weget,\\ u=\frac{1}{2}{\gamma }^2{T}^2{Y}^{-1}\end{array}$

Hence,

option $\left(A\right)$ is correct answer.