Question

Torsion applied to a circular shaft results in a twist of $1^o$ over a length of 1 m. The maximum shear stress induced is $120N/m{m}^2$ and the modulus of rigidity of the shaft material is $0.8\times {10}^{5}N/m{m}^2$. What is the radius of the shaft?

• A. $\frac{300}{\pi }$
• B. $\frac{180}{\pi }$
• C. $\frac{90}{\pi }$
• D. $\frac{270}{\pi }$

Answer 1

The correct option is D $\frac{270}{\pi }$

We know that

$\frac{\tau }{R}=\frac{G\theta }{L}$

$\Rightarrow \frac{120}{R}=\frac{0.8\times {10}^5\times 1\times \pi }{1\times {10}^3\times 180}$

$\Rightarrow R=\frac{270}{\pi }$