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 $1000kg/cm^{2}$ and if modulus of rigidity $G=0.8\times 10^{6}kg/cm^{2},$ then the radius of the shaft should be
- A. $\pi/18$ cm
- B. $\pi/27$ cm
- C. $18/\pi$ cm
- D. $27/\pi$ cm
Answer: D. $27/\pi$ cm
Explanation: Given: $l=120~cm$, $\tau=1000~kg/cm^{2}$, $G=0.8\times10^{6}kg/cm^{2}$, $\theta=1^{\circ}=1\times\frac{\pi}{180}rad$. Using the Torsion Equation: $\frac{\tau}{r} = \frac{G\theta}{l}$. Substituting the values: $\frac{1000}{r} = \frac{0.8\times10^{6}\times\pi}{180\times120}$. Solving for $r$, $r=\frac{27}{\pi} cm$.