A circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be-a)proportional to (D3)b)proportional to (D4)c)inversely proportional to (D3)d)inversely proportional to (D4)Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Explanation:

Shear Stress in a Circular Shaft:
- When a torque is applied to a circular shaft, it creates shear stress within the material.
- The formula for shear stress in a circular shaft is τ = Tc / J, where T is the torque, c is the radial distance from the center of the shaft to the outer surface, and J is the polar moment of inertia.

Relationship with Diameter:
- The polar moment of inertia, J, for a circular shaft is directly proportional to the fourth power of the diameter, D⁴ (J ∝ D⁴).
- Therefore, the shear stress (τ) is inversely proportional to the diameter cubed, as J increases with the fourth power of diameter while shear stress decreases with the third power of diameter.
- This relationship is represented by the formula τ ∝ 1/D³.

Conclusion:
- The maximum shear stress in a circular shaft subjected to a torque is inversely proportional to the cube of the diameter, making option 'C' the correct answer.

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