A) \[\frac{M{{\omega }_{0}}}{M+3m}\]
B) \[\frac{M{{\omega }_{0}}}{M+m}\]
C) \[\frac{M{{\omega }_{0}}}{M+2m}\]
D) \[\frac{M{{\omega }_{0}}}{M+6m}\]
Correct Answer: D
Solution :
Applying angular momentum conservation, about axis of rotation \[{{L}_{i}}={{L}_{f}}\] \[\frac{M{{L}^{2}}}{12}{{\omega }_{0}}=\left( \frac{M{{L}^{2}}}{12}+m{{\left( \frac{L}{2} \right)}^{2}}\times 2 \right)\omega \] \[\Rightarrow \]\[\omega =\frac{M{{\omega }_{0}}}{M+6m}.\]
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