Correct Answer - Option 4 : (shaft diameter)

^{4}
__Explanation:__

We know that **T**orsion 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

\(\theta = \frac{{TL}}{{GJ}}\)

Putting the value of ‘J’ in the above equation

\(\theta = \frac{{TL}}{G} \times \frac{{32}}{{\pi {d^4}}}\)

\(\theta \propto \frac{1}{{{d^4}}}\;\;\;\;\;\;\;\left\{ {\because T,L\;and\;G\;are\;constant} \right\}\)