With usual notations, the torsional equation for shafts of circular cross-sections is
- AT/J = τ/θ = Gr/L
- BT/r = τ/J = Gr/L
- CT/J = τ/L = Gθ/r
- DT/J = τ/r = Gθ/LCorrect
Solution
Concept
Torsion equation
Formula
T/J = τ/r = Gθ/L
Step-by-step solution
1. Shear stress τ = G γ and γ = rθ/L. 2. Torque T = τ J / r. 3. Together: T/J = τ/r = Gθ/L.
Explanation
The three ratios are equal for a solid or hollow circular shaft in the elastic range.
Why the other options are wrong
The other options misplace J, r, L or θ.
Shortcut
T/J = τ/r = Gθ/L.
Common mistake
Swapping r and J.
Correct answer: D) T/J = τ/r = Gθ/L