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 `v_0` and `2v_0` respectively as shown in the figure. Then the ratio of angular speed of upper cylinder to lower cylinder 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`