Question

A circular shaft of diameter d resists the maximum shear stress $\tau$ caused by torque T. If the same torque is applied to a shaft having diameter 2d and length half the length of shaft of diameter d, the maximum shear stress developed in shaft (having diameter 2d) is:

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

Answer 1

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

Maximum shear stress, $\tau =\frac{16T}{\pi d^3}$
Maximum shear stress developed in 2nd shaft
$=\frac{16T}{\pi (2d{)}^3}=\frac{\tau }{8}$