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A uniform wire of length \( L \) and radius \( r \) is twist by an angle \( \alpha \). If modulus of rigidity of the wire is \( \eta \), then the elastic potential energy stored in wire
P
(1) \( \frac{\pi \eta r^{4} \alpha}{2 L^{2}} \)
(2) \( \frac{\pi \eta r^{4} \alpha^{2}}{4 \mathrm{~L}} \)
W
(3) \( \frac{\pi \eta r^{4} \alpha^{2}}{4 \mathrm{~L}} \)
(4) \( \frac{\pi \eta r^{4} \alpha^{2}}{2 L} \)
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