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Q. A ring of radius $r$ is given a velocity $v _{0}$ in forward direction angular velocity $\omega=3 v _{0} / r$ in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center of mass $\left( v _{ cm }\right)$ as a function of time $t$ is :Physics Question Image

Solution:

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Sphere will move then backward and rolling will start
$m v_{0} R-I \frac{3 v_{0}}{r}=m v_{c} R+I \omega $
$v_{c}=\omega R$