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A solid cylinder of mass m and radius r rolls on fixed cylindrical surface of radius R at the instant shown line joining both the centre is rotating with angular velocity $ω$ and angular acceleration $α$ . Find the acceleration point P which is the point of the rolling cylinder in contact with the fixed cylinder.

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$ω^{2} \frac{(R - r) R}{r}$

$ω^{2} \frac{r^{2}}{R}$

$ω^{2} \frac{R^{2}}{r}$

$ω^{2} \frac{(R + r) R}{r}$

answer is A.

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Detailed Solution

$a_{c o m} = ω^{2} (R + r)$

$ω (R + r) = ω' r$

$ω' = \frac{ω (R + r)}{r}$

$a_{p c o m} = ω^{12} r$ $= \frac{ω^{2} {(R + r)}^{2}}{r}$

$a_{p} = \frac{ω^{2} {(R + r)}^{2}}{r} - ω^{2} (R + r)$ $= ω^{2} (R + r) (\frac{R + r}{r} - 1)$

$a_{p} = \frac{ω^{2} (R + r) R}{r}$

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