A sphere of mass \( m \) and radius \( r \) is pushed onto the fixe...

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A sphere of mass \( m \) and radius \( r \) is pushed onto the fixed horizontal surface such that it rolls without slipping from the beginning. Determine the minimum speed \( v \) of its mass centre at the bottom so that it rolls completely around the loop of radius \( (\mathrm{R}+\mathrm{r}) \) without leaving the track in between.
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