A uniform wire of length L and radius r is tw | vedclass

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(C) The elastic potential energy $U$ stored in a twisted wire is equal to the work done in twisting it.The formula for the work done in twisting a wir

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

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(C) The elastic potential energy $U$ stored in a twisted wire is equal to the work done in twisting it.The formula for the work done in twisting a wire of length $L$,radius $r$,and modulus of rigidity $\eta$ by an angle $\alpha$ is given by:$U = \frac{1}{2} C \alpha^2$where $C$ is the torsional rigidity (or torque constant) of the wire.The torsional rigidity $C$ is given by:$C = \frac{\pi \eta r^4}{2 L}$Substituting the value of $C$ into the energy equation:$U = \frac{1}{2} \left( \frac{\pi \eta r^4}{2 L} \right) \alpha^2$$U = \frac{\pi \eta r^4 \alpha^2}{4 L}$Thus,the correct option is $C$.

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

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