A) \[\sqrt{\frac{2gh}{I+mr}}\]
B) \[{{\left[ \frac{2mgh}{I+m{{r}^{2}}} \right]}^{1/2}}\]
C) \[{{\left[ \frac{2mgh}{I+2m{{r}^{2}}} \right]}^{1/2}}\]
D) \[\sqrt{2gh}\]
Correct Answer: B
Solution :
We know \[\text{v}=\sqrt{\frac{2gh}{1+\frac{{{k}^{2}}}{{{r}^{2}}}}}\] \[\therefore \,\,\omega =\frac{\text{v}}{r}=\sqrt{\frac{2gh}{{{r}^{2}}+{{k}^{2}}}}\] \[\omega =\sqrt{\frac{2mgh}{m{{r}^{2}}+m{{k}^{2}}}}=\sqrt{\frac{2mgh}{m{{r}^{2}}+I}}=\sqrt{\frac{2mgh}{I+m{{r}^{2}}}}\]
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