A sphere of mass `M` and radius `R` is moving on a rough fixed surface, having coefficient of friction `mu`. as shown in Fig. It will attain a minimum linear velocity after time (`v_(0)gtomega_(0)R)`

Options

A. `v_(0)//mug`
B. `omega_(0)R//mug`
C. `2(v_(0)-omega_(0)R)//5mug`
D. `2(v_(0)-omega_(0)R)//7mug`

Answer

D

Explanation

Since `v_(0)gtomega_(0)R` so bottom most point will have forward velocity initially. So friction on sphere will act in backoward direction. Minimum velocity will occur when `v=omegaR`
`impliesv_(0)-mugt=(omega_(0)+(5mug)/(2R)t)Rimpliest=(2(v_(0)-omega_(0)R))/(7mug)`