If the outer radius is halved while torque and the polar moment of inertia remain constant, how does the shear stress change?

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Multiple Choice

If the outer radius is halved while torque and the polar moment of inertia remain constant, how does the shear stress change?

Explanation:
When a shaft is under torsion, the shear stress at the outer surface is given by tau = T * c / J, where c is the outer radius and J is the polar moment of inertia. If torque and J stay the same but the outer radius is halved, the only change is c, which halves. Therefore tau becomes (T * (c/2)) / J = (1/2) * (T * c / J). So the shear stress is reduced by half.

When a shaft is under torsion, the shear stress at the outer surface is given by tau = T * c / J, where c is the outer radius and J is the polar moment of inertia. If torque and J stay the same but the outer radius is halved, the only change is c, which halves. Therefore tau becomes (T * (c/2)) / J = (1/2) * (T * c / J). So the shear stress is reduced by half.

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