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 radian/sec) of the resulting SHM? (Given $K = 4 M /3$ ).

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TestHub · Accepted Answer

For a displacement x along the plane, the restoring force along the plane is $F = - K x cos^{2} 3 0^{\circ}$

$ma = - (K cos^{2} 3 0^{\circ}) x \Rightarrow ω = \frac{3 K}{4 m}$

$ω = \frac{3}{4 m} \times \frac{4 m}{3} = 1 rad / sec$

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