A) \[\frac{\omega }{n}\]
B) \[\frac{\omega }{{{n}^{2}}}\]
C) \[n\omega \]
D) \[{{n}^{2}}\omega \]
Correct Answer: D
Solution :
From law of conservation of angular momentum, if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant that is \[J=I\omega \] Also,\[I=\frac{2}{5}M{{R}^{2}}\]for a solid sphere. Given,\[{{R}_{1}}=R,\,\,{{R}_{2}}=\frac{R}{n}\] \[\therefore \] \[\frac{2}{5}M{{R}^{2}}{{\omega }_{1}}=\frac{2}{5}M{{\left( \frac{R}{n} \right)}^{2}}\times {{\omega }_{2}}\] \[\Rightarrow \] \[{{\omega }_{2}}={{n}^{2}}{{\omega }_{1}}\] \[={{m}^{2}}\omega \]
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