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Moment of Inertia of a Disc

A system of u...

Question

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

A

1:1

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B

1:2

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C

3:2

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D

3:1

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Solution

The correct option is D
3:1

Lower cylinder

Upper Cylinder

$ω_{2} = \frac{2 V + V}{2 r} = \frac{3 V}{2 r}$

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