A uniform circular disc placed on a rough horizontal surface is initially given a velocity $v_{0}$ and angular velocity $ω_{0}$ as shown in figure. The disc comes to rest after moving some distance in the direction of motion. Then $\frac{v_{0}}{r ω_{0}}$ is:

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From conservation of angular momentum about a point on the surface, Initial angular momentum = final angular momentum: M v 0 r - 1 2 M r 2 ω 0 = 0 Therefore v 0 r ω 0 = 1 2

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