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The elastic potential energy of a wire of length \( L \) and radius \( R \) twisted by an angle \( \alpha \), modulus of rigidity of wire is \( \eta \) :
(a) \( \frac{\pi}{4} \frac{\eta R^{4} \alpha^{2}}{L} \)
(b) \( \frac{\pi R^{4} \alpha^{2}}{L} \)
(c) \( \frac{\pi^{2} R^{4} \alpha^{2}}{2 L} \)
(d) \( \frac{\pi^{2} R^{2} \alpha^{2}}{4 L} \)
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