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

Question No. 244
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, ${\theta }_{s}$ is the twist and ${\tau }_{s}$ is the maximum shear stress in the solid shaft, whereas is the twist and ${\tau }_{H}$ 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

I= IS

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