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Question

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

A
Less stiff
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B
More stiff
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C
Equally stiff
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D
None of these
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Solution

## The correct option is C More stiffThe torsion (twisting of an object by the applied force) of the uniform cross-sectional shaft is given as, τhollow=TRJandτsolid=TrJ The torsion constant for the circle is given as, J=πD432 For the two cylinders having diameters dof solid cylinder andDfor hollow cylinder then the stress is given as, τhollow=T(D/2)[π(D4o−D4i)32] For the solid cylinder the stress is, τsolid=T(d/2)[π(d4)32] 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.

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