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.
Vivek Nigam , 14 Years ago
Grade
1 Answers
Anurag Kishore
Last Activity: 14 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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