A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then

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angular velocity of the cylinder is $\frac{v}{R}$ counter clockwise

angular velocity of the cylinder is $\frac{2 v}{R}$ clockwise

velocity of centre of mass of the cylinder is v towards left

velocity ofcentre of mass of the cylinder is 2v towards right

answer is A, D.

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Detailed Solution

$L e t v e l o c i t y o f t h e c e n t r e o f m a s s b e v_{0} (t o t h e r i g h t) a n d a n g u l a r v e l o c i t y b e ω_{0} (c l o c k w i s e) T h e r e f o r e, v_{0} + R ω_{0} = v . . . (i) a n d v_{0} - R ω_{0} = 3 v . . . (i i)$

Solving these two equations, we get

$v_{0} = 2 v a n d ω_{0} = - \frac{v}{R}$

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