Topic: Strength of Materials
A circular shaft subjected to torsion undergoes a twist of $1^{\circ}$ in a length of 120 cm. If the maximum shear stress induced is limited to $1000\text{ kg/cm}^{2}$ and if the modulus of rigidity $G=0.8 \times 10^{6}\text{ kg/cm}^{2}$, then the radius of the shaft should be
- A. $\pi/18$
- B. $\pi/27$
- C. $18/\pi$
- D. $27/\pi$
Answer: D. $27/\pi$
Explanation: Given parameters are twist angle $\theta = 1^{\circ} = \frac{\pi}{180}\text{ rad}$, length $l = 120\text{ cm}$, maximum shear stress $\tau = 1000\text{ kg/cm}^{2}$, and modulus of rigidity $G = 0.8 \times 10^{6}\text{ kg/cm}^{2}$. Utilizing the torsion equation $\frac{T}{J} = \frac{G\theta}{l} = \frac{\tau}{R}$, we can rearrange the terms to solve for the radius R: $R = \frac{\tau l}{G\theta}$. Substituting the values yields $R = \frac{1000 \times 120}{0.8 \times 10^{6} \times \frac{\pi}{180}} = \frac{1000 \times 120 \times 180}{0.8 \times 10^{6} \times \pi} = \frac{27}{\pi}\text{ cm}$.