Correct Answer - Option 1 : Rigidity modulus increases
Explanation:
We know that Torsion equation is:
\(\frac{{{\tau _{max}}}}{R} = \frac{{G\theta }}{L} = \frac{T}{J}\)
where θ is the angle of twist, T = torque applied, L = length of the shaft, J = polar moment of inertia, d = diameter of the shaft
\(J = \frac{{\pi {d^4}}}{{32}}\)
From torsion equation
\(T \propto G\)
\(T \propto J\)
\(T \propto \frac 1L\)
\(T \propto \frac 1R\)
The twisting moment of a circular shaft increases when the Rigidity modulus & Polar moment of inertia Increase and the Length of the shaft & Radius of the shaft decreases.
