Question

A solid circular shaft has a diameter d. Its polar modulus will be

• A. $\frac{\pi }{16}{d}^2$
• B. $\frac{\pi }{64}{d}^3$
• C. $\frac{\pi }{16}{d}^3$
• D. $\frac{\pi }{32}{d}^2$

Answer 1

The correct option is C $\frac{\pi }{16}{d}^3$

Moment of inertia for circular shaft $=\frac{\pi d^4}{32}$

$Polarmodulus=\frac{1}{y}=\frac{\pi d^4}{32\times \frac{d}{2}}=\frac{\pi d^3}{16}$

y is the distance of maximum stress fibre from centre.