Correct Answer - Option 2 : 10
Concept:
Torsion equation
\(\frac{{{\tau }_{max}}}{r}=\frac{{{T}_{R}}}{J}=\frac{G\theta }{L}\)
\({{\tau }_{max}}=\frac{{{T}_{R}}\cdot r}{J}\)
τmax = maximum allowable shear stress
TR = Resistance torque
J = Polar moment of inertia
Calculation:
Given, T = 55 N.m = 55 × 103 N.mm
τmax = 280 N/mm2 = 280 MPa
\({{\tau }_{max}}=\frac{T\cdot r}{J}\)
\(\Rightarrow 250=\frac{55\times {{10}^{3}}\times \text{D}}{2\times \frac{\pi }{32}\times {{\text{D}}^{4}}}\)
\(\Rightarrow {{D}^{3}}=\frac{55\times {{10}^{3}}\times 32}{2\times \frac{22}{7}\times 250}\)
⇒ D = 10 mm