Question

Match List-I (Strain Energy) with List-II (Gradually applied load) and select the correct answer using the codes given below the lists $(\sigma =$ direct moment, E = Modulus of elasticity, G = Modulus of rigidity, I = Area moment of inertia, V= Volume):

List-I
A. $\frac{{\sigma }^{2}V}{2E}$
B. $\frac{{\tau }^{2}V}{2G}$
C. $\frac{{\tau }^{2}V}{4G}$
D. ${\int }_0^L\frac{M_x^{2}dx}{2EI}$

List-II

Codes :

$\begin{array}{cccc}A& B& C& D\end{array}$

• A. $\begin{array}{cccc}2& 3& 4& 1\end{array}$
• B. $\begin{array}{cccc}1& 4& 3& 2\end{array}$
• C. $\begin{array}{cccc}2& 4& 3& 1\end{array}$
• D. $\begin{array}{cccc}1& 3& 4& 2\end{array}$

Answer 1

The correct option is D $\begin{array}{cccc}1& 3& 4& 2\end{array}$

In the case of torsional load strain energy.

$U=\frac{1}{2}T\theta$

Torisonal formula is $\frac{T}{J}=\frac{G\theta }{L}=\frac{\tau }{r}$

$SoT=\frac{\tau J}{r}$

$and\theta =\frac{\tau L}{rG}$

$\therefore U=\frac{{\tau }^2}{2G}\times \left(\frac{LJ}{r^2}\right)$

Polar moment of inertia,

$J=\left(\frac{\pi r^4}{2}\right)$

$U=\frac{{\tau }^2}{2G}\times \frac{L}{2}\pi r^2$

$U=\frac{{\tau }^2}{4G}\times volume$