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A uniform disc of mass m and radius R is...

A uniform disc of mass m and radius `R` is released gentiy on a horizontal rough surface. Such that centre of the disc has velocity `V_(0)` towards right and angular velocity `omega_(0)` (anticlockwise) as shown.

Disc will certainly come back to its intial position if

Text Solution

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The correct Answer is:
7
`(momega_(0)R^(2))/2+(mR^(2))/2 omega_(0)=momega_(0)R^(2)+(mR^(2))/2omega`
`impliesomega_(0)=3/2omegaimpliesomega=(2omega_(0))/3`
`implies v=omegaR=2/3omega_(0)R=(4v_(0))/3`
`=(16v_(0)^(2))/9=v_(0)^(2)+2mugx`
`2mugx=(7v_(0)^(2))/9impliesx=(7v_(0)^(2))/(18mug)=(7omega_(0)^(2)R^(2))/(72mug)=7m`
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