Simple Harmonic Motion - Cylinder Freezes
Find the angular frequency of the small oscillations of the sphere of mass M containing water of mass m. The spring has a constant K and cylinder executes pure rolling. What happens when the water in the cylinder freezes?
K = 100 N/m M = 10 Kg m = 5 kg
The answer is 2.
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1 solution
The beauty of the question lies in the fact that the water, in the first case doesn't rotate.
Hence while writing the equations only the moment of inertia of the cylinder(hollow) is to be considered.
This can be explained as follows,
Assume that the cylinder is not completely filled. The boundary of the water always remains horizontal, and hence has no rotation. It makes absolutely no difference even if the cylinder is completely filled.
When the water freezes, the moment of inertia of the ice must be considered, since it will rotate with the cylinder.