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

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

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Machine Design
Crowning on pulley helps

In decreasing the slip of the belt
To keep the belt in centre on a pulley while it is in motion
To increase pulley life
In increasing the slip of the belt

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Machine Design
When the shaft rotates in anticlockwise direction at high speed in a bearing, it will

Move towards right of the bearing making no metal to metal contact
Move towards right of the bearing making metal to metal contact
Move towards left of the bearing making metal to metal contact
Have contact at the bottom most of the bearing

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