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 120 N/mm² and modulus of rigidity of shaft is 0.8x x 10⁵ N/mm² . What is the radius of the shaft?
1. \(\frac{{300}}{\pi }\)
2. \(\frac{{180}}{\pi }\)
3. \(\frac{{90}}{\pi }\)
4. \(\frac{{270}}{\pi }\)

Answer 1

Correct Answer - Option 4 : \(\frac{{270}}{\pi }\)

From torsion equation,

\(\frac{\tau }{r} = \frac{{G\theta }}{l} \Rightarrow \frac{{120}}{r} = \frac{{0.8 \times {{10}^5} \times \left( {\frac{\pi }{{180}}} \right)}}{{{{10}^3}}}\)

\(\Rightarrow r = \frac{{270}}{\pi }\)