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A uniform sphere of radius a rotating wi...

A uniform sphere of radius a rotating with an angular velocity `omega` about an axis perpendicualr to the plane of motion and its cener impinges on a horizontal plane, let u and v are horizontal and vertical component of velocity before impact. Then

A

if u = a`omega`, then u and `omega` are unaltered

B

if u = a`omega`, then surface is frictionless

C

If ugt a`omega`, then angular velocity increases

D

all of the above

Text Solution

AI Generated Solution

To solve the problem of a uniform sphere of radius \( a \) rotating with an angular velocity \( \omega \) about an axis perpendicular to the plane of motion, and its center impinging on a horizontal plane, we need to analyze the components of velocity before the impact and the implications of the conditions given. ### Step-by-Step Solution: 1. **Identify the Components of Velocity:** - Let \( u \) be the horizontal component of velocity before impact. - Let \( v \) be the vertical component of velocity before impact. ...
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