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

1 / 3

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Solution

The correct option is B $3$

Ggiven system is symmectric so that angular velocity will symmectric as well.
for point A:
$ω$ at point A:
$v_{A} = 2 v = v_{c m} + R ω$
$ω_{u p p e r} = \frac{3 v}{2 R}$ .....(1)

For point B:
$ω_{l o w e r} = \frac{v}{2 R}$ ....(2)

On comparing (1) and (2)
$\frac{ω_{u p p e r}}{ω l o w e r} = \frac{\frac{3 v}{2 R}}{\frac{v}{2 R}} = 3$

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