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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.

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.

Grade:

1 Answers

Anurag Kishore
37 Points
11 years ago

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

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