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Vivek Nigam Grade:
        A sphere of mass 'm' and radius 'r' is rolling without slipping on a concave surface of radius 'R',,where R>r.It makes small oscillations about lowest point.Find the time period of these oscillations.


7 years ago

Answers : (1)

Anurag Kishore
37 Points
										

I will take the sphere hollow.


 


Take at any position making angle @ with horizontal about centre of curvature of concave surface


At this instant linear acceleration of sphere


a = g sin@/(1+ k2/ r2)


For pure rolling


w r = w' (R - r)


differentiate it to get alpha (angular accln)


for pure rolling


alpha = a/r


Now use torque eqn

7 years ago
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