Question

The outside diameter of a hollow shaft is thrice to its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter is:

• A. 80/81
• B. 1/81
• C. 8/9
• D. 1/9

Answer 1

Answer:

A. 80/81

Given: $D_{0} = 3D_{i}, D_{s} = D_{0}$ (Solid shaft diameter is equal to an outer diameter of hollow shaft), Material is the same for the hollow and solid shaft (i.e. G is the same for both because G depends upon the material). $\frac{T}{\tau}=\frac{G\theta}{L}$ $T \propto J(\theta,G,L)$ = same for both or constant $\Rightarrow \frac{T_H}{T_s} =\frac{J_H}{J_s} = \frac{\frac{\pi}{32} (D_{0} ^ 4 - D_{i} ^ 4)}{\frac{\pi}{32} (D_{s}) ^ 4}$ $\Rightarrow \frac{J_{H}}{J_{s}} = 80/81$