8.Mechanical Properties of Solids
medium

A uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If modulus of rigidity of the wire is $\eta$, then the elastic potential energy stored in wire, is .........

A

$\frac{\pi \eta r^4 \alpha}{2 L^2}$

B

$\frac{\pi \eta r^4 \alpha}{4 L^2}$

C

$\frac{\pi \eta r^4 \alpha^2}{4 L}$

D

$\frac{\pi \eta r^4 \alpha^2}{2 L}$

Solution

(c)

$U=$ work done

We know

Work done $=\frac{\pi S r^4 \phi^2}{4 L}$ $\left\{\begin{array}{l}\text { Where, } \\ \phi=\text { Angle of twist }=\alpha \\ S=\text { Modulus of rigidity }=4\end{array}\right.$

Substituting values

$U=\frac{\pi \eta r^4 \alpha^2}{4 L}$

Standard 11
Physics

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