A solid sphere (radius = R) rolls without slipping in a cylindrical vessel (radius = 5R). Find the angular frequency of small oscillations of the sphere in s –1 . Take R = 
m and g = 10 m/s 2 . (axis of cylinder is fixed and horizontal).
Text Solution
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CHECK THE SOLUTION.
( 5)
For pure rolling to take place,
v = R ω
ω ' = angular velocity of COM of sphere C about O
= 
= 
= 
∴ 
= 
⇒ α′ = 
or α = 
for pure rolling
where, a = 
= 
as, Ι = 
mR 2
For small θ , sin θ θ , being restoring in nature.
α ' = 
∴ ω = 
= 
= 5
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