A) \[\frac{{{I}_{2}}\,\,\omega }{{{I}_{1}}+{{I}_{2}}}\]
B) \[\omega \]
C) \[\frac{{{I}_{1}}\,\,\omega }{{{I}_{1}}+{{I}_{2}}}\]
D) \[\frac{({{I}_{1}}+{{I}_{2}})\,\omega }{{{I}_{1}}}\]
Correct Answer: C
Solution :
According to conservation of angular momentum \[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\] \[\Rightarrow \] \[{{I}_{1}}\omega =({{I}_{1}}+{{I}_{2}}){{\omega }_{2}}\] \[\Rightarrow \] \[{{\omega }_{2}}=\frac{{{I}_{1}}\omega }{{{I}_{1}}+{{I}_{2}}}\]
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