A) \[10.8\text{ }m/s\]
B) \[~5.4\text{ }m/s\]
C) \[~2.5\text{ }m/s\]
D) none of these
Correct Answer: B
Solution :
Key Idea: Potential energy is converted into kinetic energy of rotation. From law of conservation of energy, we have the potential energy of rod when it is vertical is converted to kinetic energy of rotation. \[\therefore \] \[\frac{M}{2}gl=\frac{1}{2}I{{\omega }^{2}}\] Moment of inertia of a thin rod is \[I=\frac{1}{3}M{{l}^{2}}\] \[\frac{M}{2}gl=\frac{1}{2}\frac{M{{l}^{2}}}{3}{{\omega }^{2}}\] \[\Rightarrow \] \[\omega =\sqrt{\frac{3g}{l}}\] Given, \[l=1\,m\] \[\omega =\sqrt{3g}\] Also, \[v=r\omega \] \[\Rightarrow \]\[v=1\times \sqrt{3\times 9.8}=5.4\,m/s.\]You need to login to perform this action.
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