A system of identical cylinders and plates is shown in Fig. 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 Fig. Then the ratio of angular speeds of the upper cylinders to lower cylinders is

Options

A. `1/3`
B. `3`
C. `1`
D. none of the above

Answer

B

Explanation

Angular velocity of the upper cylinder is
`omega_(up)=(2v-(-v))/(2R)=(3v)/(2R)`, for the lower cylinder
`omega_("lower") =(v-0)/(2R)=v/(2R)`
Hence ratio `omega_("up")/omega_("lower")=3`