A) \[\frac{2}{7}{{v}_{0}}\]
B) \[\frac{3}{7}{{v}_{0}}\]
C) \[\frac{5}{7}{{v}_{0}}\]
D) \[\frac{6}{7}{{v}_{0}}\]
Correct Answer: C
Solution :
Angular momentum will remain conserved along point of contact, \[I\omega =\] constant \[m{{v}_{0}}r\,=mvr+\frac{2}{5}\,m{{r}^{2}}\times \omega \,\,(\therefore \,\,\omega =\,\frac{v}{r})\] \[m{{v}_{0}}r\,=mvr+\frac{2}{5}m{{r}^{2}}\times \frac{v}{r}\Rightarrow \,{{v}_{0}}=v+\frac{2}{5}v\] \[{{v}_{0}}=\frac{7}{5}v\,\Rightarrow \,v=\frac{5}{7}\,{{v}_{0}}\]
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