GATE Papers >> Mechanical >> 2016 >> Question No 244

Question No. 244 Mechanical | GATE 2016
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, θs is the twist and τs is the maximum shear stress in the solid shaft, whereas θis the twist and τH is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

Answer : (D) $ {\mathrm\theta}_\mathrm S={\mathrm\theta}_\mathrm H $ and $ \tau_S<\tau_H $

Solution of Question No 244 of GATE 2016 Mechanical Paper


Means diameter of hollow & solid shaft are not same and DH > DS

$ \style{font-family:'Times New Roman'}{\mathrm\tau\propto\frac1{\mathrm D^3}\;\mathrm{and}\;\mathrm\theta=\frac{\mathrm{TL}}{\mathrm{GI}}} $

Independent of diameter 

If I is same

Hence $ \style{font-family:'Times New Roman'}{{\mathrm\tau}_\mathrm H<{\mathrm\tau}_\mathrm S} $ and $ \style{font-family:'Times New Roman'}{\mathrm\theta={\mathrm\theta}_\mathrm s} $


Axial local distribution


Torsional load distribution.

Critical paint on the circumference

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