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Question

A system of uniform cylinders and plates is shown in the figure. All the cylinders are identical and there is no slipping at any contact. Velocity of lower and upper plate is v0 and 2v0 respectively as shown in the figure. Then the ratio of angular speed of upper cylinder to lower cylinder is
949422_7a8c270286754f0eb92b41405fa2ecbb.png

A
1:3
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B
3
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C
1:2
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D
2:1
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Solution

The correct option is B 3
Angular velocity of the upper cylinder can be given as:
ωup=2v(v)2R=3v2R;
and for the lower cylinder, it can be given as:
ωlower=v02R=v2R
Hence, ratio, ωupωlower=3v2Rv2R
ωupωlower=3vv=3
Hence, the correct option is (B)

1500675_949422_ans_57c41b5cd7324a09be6c9d9d7ad939f3.png

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