A) \[T=2\pi \sqrt{\frac{l}{g}}\]
B) \[T=2\pi \sqrt{\frac{2l}{g}}\]
C) \[T=2\pi \sqrt{\frac{l}{3g}}\]
D) \[T=2\pi \sqrt{\frac{2}{3}\frac{l}{g}}\]
Correct Answer: D
Solution :
[d]: The torque\[=I\alpha \] The restoring torque \[I\frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-mg\frac{l\theta }{2}\] \[\frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-\left( \frac{mgl/2}{m{{l}^{2}}/3} \right)\theta =-\left( \frac{3g}{2l} \right)\theta \Rightarrow \frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-{{\omega }^{2}}\theta \]where,\[\omega =\sqrt{3g/2l}\] \[\therefore \]\[T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{2}{3}\frac{l}{g}}\]
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