A) \[r\sqrt{\frac{3}{2gh}}\]
B) \[r\sqrt{\frac{3}{4gh}}\]
C) \[\frac{1}{r}\sqrt{\frac{4gh}{3}}\]
D) \[\frac{1}{r}\sqrt{\frac{2gh}{3}}\]
Correct Answer: C
Solution :
[c] \[mgh=\frac{1}{2}m{{v}^{2}}+\frac{1}{2}l{{\omega }^{2}}\] \[=\frac{1}{2}m{{(\omega r)}^{2}}+\frac{1}{2}\times \frac{m{{r}^{2}}}{2}\times {{\omega }^{2}}\] \[\Rightarrow mgh=\frac{3}{4}m{{\omega }^{2}}{{r}^{2}}\] \[\Rightarrow \omega =\sqrt{\frac{4gh}{3{{r}^{2}}}}=\frac{1}{r}\sqrt{\frac{4gh}{3}}\]
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