question_answer

A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of \[30{}^\circ \]from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad \[{{s}^{-1}}\]) will be (\[g=10\text{ }m{{s}^{-2}}\]) [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) \[\sqrt{\frac{30}{2}}\]                                   

B) \[\frac{\sqrt{20}}{3}\]

C) \[\frac{\sqrt{30}}{2}\]           

D)               \[\sqrt{30}\]

Correct Answer: D

Solution :

\[mg\frac{L}{2}\,sin\,30{}^\circ \text{ }=\text{ }\frac{1}{2}\text{ }I{{\omega }^{2}}\] \[\frac{mgL}{4}=\frac{1}{2}\,\times \,\frac{1}{3}\,m{{L}^{2}}{{\omega }^{2}}\] \[{{\omega }^{2}}\,=\,\frac{3g}{2\,L}\] \[\omega \,=\,\sqrt{30}\,\,rad/s\]