Question

The upper end of a wire of radius 4 mm and length $100$ cm is clamped and its other end is twisted through an angle of $30^{\circ }$. The angle of shear is

• A. $12^{\circ }$
• B. $1.2^{\circ }$
• C. $0.12^{\circ }$
• D. $0.012^{\circ }$

Answer 1

Answer: (C)

Angle of twist at free end
$=30^{\circ }=\frac{30}{180}\times \pi$ rad $=\frac{\pi }{6}$ rad
Displacement of the free surface,
$\Delta L=\frac{2\pi r}{2\pi }\times \frac{\pi }{6}=\frac{\pi r}{6}=\frac{\pi \times 0.4}{6}cm$
Angle of shear or shearing strain $=\frac{\Delta L}{L}$
$=\frac{\pi \times 0.4}{6\times 100}$ rad.
$=\frac{\pi \times 0.4}{6\times 100}\times \frac{180}{\pi }$
degree $=0.12^{\circ }$