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utkarshakash
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Homework Statement
A sphere of mass M and radius R is moving on a rough fixed surface, having co-efficient of friction μ, with a velocity v towards right and angular velocity ω clockwise. It will attain a minimum linear velocity at time (take v>ωR)
The Attempt at a Solution
Since v>ωR the sphere rolls with slipping. So frictional force will act in the backward direction. Using the equation [itex]\int \tau dt = \int dL [/itex] where τ=μmgR.
[itex]\mu mgRt= \frac{2}{5} mR^2 (\omega ' - \omega) \\
\mu mg = m \frac{dv}{dt} \\
\mu gt = (v' - v)
[/itex]
Using the relation v'=ω'R and solving the above two equations I get
t= 2(v-ωR)/3μg. But the correct answer has 7 in the denominator.