A) \[\frac{1}{4}\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{3}\]
D) \[\frac{2}{3}\]
Correct Answer: C
Solution :
Translation kinetic energy, \[{{K}_{1}}=\frac{1}{2}\,\,m{{v}^{2}}\] \[=\frac{1}{2}\,\,m\,{{r}^{2}}\times {{\omega }^{2}}\] Rational kinetic energy, \[{{K}_{2}}=\frac{1}{2}\,\,I\,{{\omega }^{2}}\] \[=\frac{1}{2}\times \frac{1}{2}m\,{{r}^{2}}\,\,{{\omega }^{2}}=\frac{1}{2}m\,{{r}^{2}}{{\omega }^{2}}\] Total kinetic energy, \[K={\scriptstyle{}^{3}/{}_{4}}m{{r}^{2}}{{\omega }^{2}}\] \[\frac{{{K}_{2}}}{K}=\frac{1}{4}\times \frac{4}{3}=\frac{1}{3}\]
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