A bobbin is pushed along on a rough stationary horizontal surface as shown in the figure. The board is kept horizontal and there is no slipping at any contact points. The distance movedby the board when distance moved by the axis of the bobbin is `l` is
.

Options

A. `l(1 + (r)/(2 R))`
B. `l(2 + (r)/(2 R))`
C. `l(1 + (r)/(R))`
D. `l(1 + (2r)/(R))`

Answer

C

Explanation

( c) For no slipping , `v_(cm) = omega R`
`v_B = omega r + v_(cm) = v_(cm)(1 + (r)/(R))`
`(l _B)/(l) = (v_B)/(v_(cm)) = (1 + (r)/(R)) rArr l_B = l (1 + (r)/(R))`.