A) \[n\propto m\,{{R}^{2}}\]
B) \[2\pi n\propto n{{R}^{2}}\]
C) \[\frac{1}{2}\,mn\propto {{R}^{2}}\]
D) \[mn\propto {{R}^{2}}\]
Correct Answer: B
Solution :
For uniform angular acceleration in a circular path, the angular speed is given by \[{{\omega }^{2}}={{\omega }^{2}}_{0}+2\alpha \theta =0+2\alpha \,(2\pi n)\] Kinetic energy of the particle \[KE=\frac{1}{2}m\] \[{{(R\omega )}^{2}}=\frac{1}{2}m{{R}^{2}}\,(4a\,\pi n)\] \[=2\pi nm\,\alpha {{R}^{2}}\]
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