Question

A long wire hangs vertically with its upper end clamped. A torque of $8Nm$ applied to the free end twists it through ${45}^{\circ }$. The potential energy of the twisted wire is

• A. $\pi J$
• B. $\frac{\pi }{2}J$
• C. $\frac{\pi }{4}J$
• D. $\frac{\pi }{8}J$

Answer 1

The correct option is A $\pi J$

the elastic potential energy twisted by a torque T by an angle $\theta$

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

$U=\frac{8\times \frac{\pi }{4}}{2}=\pi J$