A uniform solid sphere of radius R is placed on a rough horizontal surface and given a linear velocity $v_{0}$ and angular velocity $ω_{0}$ as shown. The sphere comes to rest after moving some distance to the right. It follows that

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$v_{0} = ω_{0} R$

$2 v_{0} = 5 ω_{0} R$

$5 v_{0} = 2 ω_{0} R$

$2 v_{0} = ω_{0} R$

answer is C.

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Detailed Solution

$f = μ m g, a = μ g$

$α = \frac{μ m g R}{\frac{2}{5} m R^{2}} = \frac{5}{2} \frac{g μ}{R}$

Now, $t = \frac{V_{0}}{a} = \frac{ω_{0}}{α}$ or $\frac{a}{α} = \frac{V_{0}}{ω_{0}}$
$∴ \frac{2 R}{5} = \frac{V_{0}}{ω_{0}}$
$∴ 5 V_{0} = 2 ω_{0} R$

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