There are four arrangements of a solid cylinder and a plank as shown in the figures. Some surfaces are smooth and some are rough as indicated . There is no slipping at each rough surface. The plank and `//` or centre of cylinder are given a horizontal constant velocity as shown in each of the situations. Usinn this information fill in the blanks.
The speed of center of mass of the cylinder is `.........................`.
`(ii)` , The angular velocity of the cylinder is `.......................`.
`(iii)`,`(RES_PHY_DPP_04_XI_E01_537_Q03.png" width="80%"> The speed of center of mass of the cylindr is `...............` .
`(iv)`, The angular velocity of the cylinder is `............` .
`(a) V`
`(b) V//R`
`(c) 2V//R`
`(d) 4V//R`
`(e)` cannot be determined from the given information
`(f)` Zero.

Options

A. `(i)d (ii)b (ii)f(iv)c`
B. `(i)e (ii)v(iii)f(iv)b`
C. `(i)e(ii)d(iii)f(iv)c`
D. `(i)e (ii)v(iii)f(iv)a`

Explanation

`V_(cm)=omegaR=V, V_(cm)=V-omegaR`
`omega` depends on value of friction between plank `&` cylinder, hence `V_(cm)` is undetermined.
`(ii) omega=(2v)/(2R)=(V)/(R)`
`(ii)omega=(2V)/(2R)=(V)/(R), ` hence `V_(cm)=0`
`(iv) omega _(A//C)=(3V+V)/(R)=(4V)/(R)rArr omega=(4V)/(R)`