Machine Design
The ball bearings are provided with a cage

To prevent the lubricant from flowing out
To facilitate slipping of balls
To maintain the balls at a fixed distance apart
To reduce friction

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Machine Design
The angle of twist of shaft is

Directly proportional to (shaft diameter)²
Inversely proportional to (shaft diameter)²
Inversely proportional to (shaft diameter)⁴
Directly proportional to (shaft diameter)⁴

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