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Question

# The maximum shear stress in a solid shaft of circular cross-section having diameter d subjected to a torque T is τ. If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

A
2 τ
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B
τ
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C
τ/2
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D
τ/4
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Solution

## The correct option is C τ/2By torsion formula, τr=TJ Where, τ = shear stress r = radius of shaft T = Torsional moment J = Polar moment of inertia For solid circular shaft, J=πd432 τ=T.rJ=T.(d2)(πd432) ⇒τ=16Tπd3 Now, T1=4T and, d1=2d τ1=16(4T)π(2d)3=12(16Tπd3) τ1=τ2

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