Question

Two shafts one is solid circular cross section and another is thin circular cross-section having same diameter. What is the thickness of shaft if both subjected to same torque?

• A. $\frac{D}{8}$
• B. $\frac{D}{4}$
• C. $\frac{D}{2}$
• D. $\frac{D}{16}$

Answer 1

The correct option is A $\frac{D}{8}$

We know that,


$\frac{T}{J}=\frac{\tau }{R}$

Let D is the diameter for both the shaft, For thin circular shaft,

$J=\frac{\pi D^{3}t}{4}$

$T_c=\frac{\pi D^{3}t}{4\times D}\times 2\times \tau$

$T_c=\frac{\pi D^{2}t}{2}\tau$

For solid shaft, $T_s=\frac{\pi }{16}\tau D^3$

Given $T_c=T_{s}and\tau$ is same for both shaft as material is same

$\frac{\pi D^{2}t}{2}\tau =\frac{\pi }{16}\tau \times D^3$

$t=\frac{D}{8}$