Machine Design
A key way lowers

Both the strength and rigidity of the shaft
The ductility of the shaft
The rigidity of the shaft
The strength of the shaft

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Machine Design
The shear stress at a point in a shaft subjected to a torque is

Directly proportional to the applied torque and the polar moment of inertia
Directly proportional to the applied torque and inversely proportional to the polar moment of inertia
Directly proportional to the polar moment of inertia and to the distance of the point from the axis
Inversely proportional to the applied torque and the polar moment of inertia

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