Machine Design
The stiffness of a closely coiled helical spring subjected to an axial load W is equal to (where G = Modulus of rigidity, and n = Number of active coils)

Gd⁴/ 4D3n
Gd⁴/ 8D²n
Gd⁴/ 8D3n
Gd3/ 8D3n

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

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

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Machine Design
The effective stress in wire ropes during normal working is equal to the stress due to

Axial load plus stress due to acceleration/retardation
Bending plus stress due to acceleration/retardation
Acceleration/retardation of masses plus stress due to bending
Axial load plus stress due to bending

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