First slide

Rolling motion

Question

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 moved by the board when distance moved by the axis of the bobbin is l is

Moderate

A

$l (1 + \frac{r}{2 R})$
B

$l (2 + \frac{r}{R})$
C

$l (1 + \frac{r}{R})$
D

$l (1 + \frac{2 r}{R})$

Solution

For no slipping, $v_{cm} = ωR - - - - (i)$
$v_{B} = ωr + v_{cm} = v_{cm} (1 + \frac{r}{R})$ -------(ii)
$\frac{l_{B}}{l} = \frac{v_{B}}{v_{cm}} = (1 + \frac{r}{R}) \Rightarrow l_{B} = l (1 + \frac{r}{R})$

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