Question

A solid shaft of circular cross-section is subjeted to torque T which produces a maximum shear stress $\tau$ in the shaft. The diameter of the shaft will be

• A. $3\sqrt{\frac{16T}{\pi \tau }}$
• B. $\sqrt{\frac{\pi \tau }{16T}}$
• C. $3\sqrt{\frac{\pi \tau }{16T}}$
• D. $\sqrt{\frac{16T}{\pi \tau }}$

Answer 1

The correct option is A $3\sqrt{\frac{16T}{\pi \tau }}$

For a solid shaft

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

$\Rightarrow \frac{T}{\pi D^4/32}=\frac{\tau }{D/2}$

$\Rightarrow \tau =\frac{16T}{\pi D^3}$

$D^3=\frac{16T}{\pi \tau }$

$\Rightarrow D=3\sqrt{\frac{16T}{\pi \tau }}$