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A system of identical cylinders and plates is shown in figure. All the cylinders are identical and there is no slipping at any contact. The velocity of lower and upper plates are v and 2v, respectively, as shown in figure. Then the ratio of angular speeds of the upper cylinders to lower cylinders is

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Detailed Solution

Angular velocity of the upper cylinder is

$\begin{array}{l} ω_{up} = \frac{2 v - (- v)}{2 R} = \frac{3 v}{2 R}; for the lower cylinder \\ ω_{lower} = \frac{v - 0}{2 R} = \frac{v}{2 R} \end{array}$

Hence, ratio, $\frac{ω_{up}}{ω_{lower}} = 3$

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