A) \[\frac{k}{2I}\theta \]
B) \[\frac{k}{I}\theta \]
C) \[\frac{k}{4I}\theta \]
D) \[\frac{2k}{I}\theta \]
Correct Answer: D
Solution :
Kinetic energy \[KE=\frac{1}{2}I{{\omega }^{2}}=k{{\theta }^{2}}\] \[\Rightarrow {{\omega }^{2}}=\frac{2k{{\theta }^{2}}}{I}\Rightarrow \omega =\sqrt{\frac{2k}{I}}\theta \] ?(1) Differentiate (1) wrt time\[\to \] \[\frac{d\omega }{dt}=\alpha =\sqrt{\frac{2k}{I}}\left( \frac{d\theta }{dt} \right)\] \[\Rightarrow \]\[\alpha =\sqrt{\frac{2k}{I}}.\sqrt{\frac{2k}{I}}\theta \{by\,(1)\}\] \[\Rightarrow \alpha =\frac{2k}{I}\theta \] OptionYou need to login to perform this action.
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