A) \[\frac{1}{8}m{{v}^{2}}\]
B) \[\frac{1}{4}m{{v}^{2}}\]
C) \[\frac{1}{3}m{{v}^{2}}\]
D) \[m{{v}^{2}}\]
Correct Answer: B
Solution :
Kinetic energy of rotation of a body having moment of inertia \[I\] and angular velocity \[\omega \]is given by \[K=\frac{1}{2}I{{\omega }^{2}}\] For a circular ring of radius r, and mass m moment of inertia\[(I)\]about its diameter is given by \[I=\frac{M{{r}^{2}}}{2}\] \[\therefore \] \[K=\frac{1}{2}{{\left( \frac{M{{r}^{2}}}{2} \right)}^{2}}{{\omega }^{2}}\] Also,\[v=r\omega ,\]therefore \[\omega =\frac{v}{r}\] \[\therefore \] \[K=\frac{1}{2}\left( \frac{m{{r}^{2}}}{2} \right){{\left( \frac{v}{r} \right)}^{2}}=\frac{1}{4}m{{v}^{2}}\]
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