| A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30: from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal \[(\text{in}\,\text{rad}\,{{\text{s}}^{-\,1}})\]will \[(g=10\text{m}{{\text{s}}^{-\,2}}).\] |
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A) \[\sqrt{\frac{30}{2}}\]
B) \[\sqrt{30}\]
C) \[\sqrt{\frac{20}{2}}\]
D) \[\sqrt{\frac{30}{2}}\]
Correct Answer: B
Solution :
\[mg\frac{\ell }{2}\left( \frac{1}{2} \right)=\frac{1}{2}\left( \frac{m\ell }{3} \right){{\omega }^{2}}\] \[\Rightarrow \] \[\omega =\sqrt{\frac{3g}{2\ell }}=\sqrt{30.}\]
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