Q.

A sphere of mass M and radius R is on a smooth fixed inclined plane in equilibrium as shown in the figure. If now the sphere is displaced through a small distance along the plane, what will be the angular frequency (in rads-1) of the resulting SHM?  Given, k=4M3

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Detailed Solution

If the sphere moves down along the plane by a distance x, extension in the spring = x cos 30o∴ Restoring force = F cos 30o=kxcos⁡30∘cos⁡30∘=kx322=34kxAs it is restoring in nature FR=−34kxa=−34⋅kMxω=34⋅kM=34M⋅4M3=1rads−1
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