Question

A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at the free end is

• A. $\frac{16TL}{\pi d^{4}G}$
• B. $\frac{32TL}{\pi d^{4}G}$
• C. $\frac{64TL}{\pi d^{4}G}$
• D. $\frac{128TL}{\pi d^{4}G}$

Answer 1

The correct option is B $\frac{32TL}{\pi d^{4}G}$



$\frac{T}{J}=\frac{G\theta }{L}$
Where J = Polar moment of inertia
For circular section
$J=\frac{\pi d^4}{32}$
$\theta =\frac{TL}{GJ}$
$=\frac{TL32}{G\pi d^4}$
$=\frac{32TL}{\pi d^{4}G}$