A solid sphere (radius = R) rolls without slipping in a cylindrical through (radius = 5R). Find the time period of small oscillations.
2π√28R5g
For pure rolling to take place,
v=Rωω′=angular velocity of COM of sphere C about Ov4R=Rω4R=ω4∴dω′dt=14dωdtor α′=α4α=aR for pure rollingwhere, a=gsinθ1+ImR2=5gsinθ7as, I=25mR2∴α′=5gsinθ28RFor small θ,sinθ≈θ, being restoring in nature,α′=−5g28Rθ∴T=2π√∣∣θα′∣∣=2π√28R5g