Question

The ratio of torsional moments or resistance of a solid circular shaft of diameter D to that of a hollow shaft with external diameter D and internal diameter d.Both the shafts are of the same material.

• A. $\frac{D^4}{D^4-d^4}$
• B. $\frac{D^4-d^4}{D^4}$
• C. $\frac{D^3}{D^3-d^3}$
• D. $\frac{D^3-d^3}{D^3}$

Answer 1

The correct option is A $\frac{D^4}{D^4-d^4}$

The polar modulus for a solid circular shaft

$Z_1=\frac{\pi D^3}{16}$

Polar modulus for a hollow shaft

$Z_2=\pi \frac{(D^4-d^4)}{16D}$

$\therefore \frac{Z_1}{Z_2}=\frac{\pi D^3}{16}\times \frac{16D}{\pi (D^4-d^4)}$

$=\frac{D^4}{D^4-d^4}$