Question

Prove that a hollow cylindrical shaft is stronger than a

solid shaft of same mass, length and material.​

Answer 1

Answer:

A hollow shaft is found to be stronger than a solid shaft made of the same size and material. Reason: The torque required to produce a given twist in a hollow cylinder is greater than that required to twist a solid cylinder of the same size and material.

Answer 2

Answer:

A hollow cylindrical shaft is stronger than a solid shaft of same mass, length and material.​

Explanation:

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

$\tau_{hollow}=\dfrac{TR}{J}$

​and

$\tau_{solid}=\dfrac{Tr}{J}$

​The torsion constant for the circle is

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

For the two cylinders having diameters $dof$ solid cylinder and $D$

For a hollow cylinder then the stress is

$\tau_{hollow}=\dfrac{T\dfrac{D}{2}}{\pi(\dfrac D^{4} -D_{i}^{4})\(32)}$

​For the solid cylinder the stress is

$\tau_{solid}=\frac{T(d/2)}{\pi(\dfrac{d^4}{32})}$

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

Hence,  a hollow is stiffer than solid cylinder.

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