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 :
Let, the final velocity be v So, angular momentum will remain conserved along point of contact By conservation of angular momentum Angular momentum will remain conserved along point of contact \[I\omega =\text{cosntant}\] \[m{{v}_{0}}r=mvr+\frac{2}{5}m{{r}^{2}}\times \omega \] \[\left( \because \,\omega =\frac{v}{r} \right)\] \[m{{v}_{0}}r=mvr+\frac{2}{5}m{{r}^{2}}\left( \frac{v}{r} \right)\] \[{{v}_{0}}=v+\frac{2}{5}v\] \[{{v}_{0}}=\frac{7}{5}v\Rightarrow v=\frac{5}{7}{{v}_{0}}\]You need to login to perform this action.
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