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a solid sphere{radius R ) ROLLS WITHOUT SLIPPING IN A CYLINDERCAL THROUGH (RADIUS 5R). FIND THE TIME PERIOD OF SMALL OCSILLATIONS.

HIMANSHU AGARWAL , 13 Years ago
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pavani suhani

Last Activity: 13 Years ago

let the COM of the sphere has a velocity V=Rω, where ω is the angular velocity of sphere wrt the COM.Let the angular velocity of the sphere wrt the centre of the cylinder be W then V=(5R-R)W

 

                                                                                  W=ω/4

                                                   from conservation of energy

mg(5R-R)(1-cosθ)+(1/2)mV^2+(1/2)Iω^2=constant

differentiating the above equation wrt time we get( α/θ)=5g/28R

therefore time period =2π(k)^1/2,where k=28R/5g

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