A) \[2\pi \sqrt{\frac{M}{6k}}\]
B) \[2\pi \sqrt{\frac{M}{3k}}\]
C) \[2\pi \sqrt{\frac{ML}{k}}\]
D) \[\pi \sqrt{\frac{M}{6k}}\]
Correct Answer: A
Solution :
[a] The restoring torque \[\left( for\text{ }small\text{ }\theta \right)\] \[{{\tau }_{rest}}=-\left[ \frac{kL\theta }{2}\times \frac{L}{2} \right]\times 2=\frac{k{{L}^{2}}}{2}(-\theta )\] \[\therefore \,\alpha =\frac{{{\tau }_{rest}}}{I}=\frac{k{{L}^{2}}/2}{M{{L}^{2}}/12}(-\theta )=\frac{6k}{M}(-\theta )\] \[\therefore \,\,T=2\pi \sqrt{\frac{M}{6k}}\].You need to login to perform this action.
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