Question

The hollow shaft is _____ than a solid of same mass, material and length.

• A. Less stiff
• B. More stiff
• C. Equally stiff
• D. None of these

Answer 1

Answer: (B)

More stiff

The torsion (twisting of an object by the applied force) of the uniform cross-sectional shaft is given as,

${\tau }_{hollow}=\frac{TR}{J}$and${\tau }_{solid}=\frac{Tr}{J}$

The torsion constant for the circle is given as,

$J=\frac{\pi D^4}{32}$

For the two cylinders having diameters $d$of solid cylinder and$D$for hollow cylinder then the stress is given as,

${\tau }_{hollow}=\frac{T\left(D/2\right)}{\left[\pi \frac{\left(D_o^4-D_i^4\right)}{32}\right]}$

For the solid cylinder the stress is,

${\tau }_{solid}=\frac{T\left(d/2\right)}{\left[\pi \frac{\left(d^4\right)}{32}\right]}$

Since the twisting couple for a hollow cylinder is greater than that of the solid cylinder having same mass, length and material. Hence hollow is more stiffer than solid cylinder.