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A uniform circular disc of radius R rolls without slipping with its center of mass moving along positive X-axis with a speed v. The velocity of point P at the instant shown in figure is

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$V_{P} = V + \frac{Vr sinθ}{R} i + \frac{Vr cosθ}{R} j$

$V_{P} = V + \frac{Vr sinθ}{R} i - \frac{Vr cosθ}{R} j$

$V_{P} = (V + \frac{Vr sinθ}{R}) i + \frac{Vr cosθ}{R} j$

$V_{P} = (V + \frac{Vr sinθ}{R}) i - \frac{Vr cosθ}{R} j$

answer is B.

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Detailed Solution

$ω = \frac{V}{R}$

$\vec{V_{p}} = V \hat{i} + \vec{r} \times \vec{ω}$

$\Rightarrow \vec{V_{p}} = V \hat{i} + (rcosθ \hat{i} + rsinθ \hat{j}) \times (\frac{V}{R} \hat{k})$

$V_{P_{x}} = (V + \frac{V}{R} rsinθ) \hat{i}$ , $V_{P_{y}} = - \frac{V}{R} rcosθ \hat{j}$

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