A) \[\frac{\omega }{2n}\]
B) \[\frac{\omega }{{{n}^{2}}}\]
C) \[n\omega \]
D) \[{{n}^{2}}\omega \]
Correct Answer: D
Solution :
In this case angular momentum remains conserved. According to law of conservation of angular momenutm, when no external torque is acting upon a body rotation about as axis then the angular momentum of the body remains constant that is: \[J=I\omega .\] Where I is moment of Inertia and co the angular velocity Also, \[I=\frac{2}{5}M{{R}^{2}}\] for a solid sphere Here, \[{{R}_{1}}=R,\,{{R}_{2}}=\frac{R}{n}\] \[\therefore \] \[\frac{2}{5}M{{R}^{2}}{{\omega }_{1}}=\frac{2}{5}M{{\left( \frac{R}{n} \right)}^{2}}\times {{\omega }^{2}}\] \[\Rightarrow \] \[{{\omega }_{2}}={{n}^{2}}{{\omega }_{1}}.\] Here, \[{{\omega }_{1}}=\omega ,\] therefore \[{{\omega }^{2}}={{n}^{2}}\omega \]
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