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

• A. ℓR
• B. ℓr
• C.
• D.

Answer 1

The correct option is C

$V_B=\omega r+V_{CM}$

Let time taken be t, then

$\ell =V_{CM}\times t$

$\Rightarrow t=\frac{l}{V_{CM}}$

Distance moved by board

$d=V_B\times t$

$=(\omega r+V_{CM})\frac{l}{V_{CM}}$

$V_{CM}=\omega R$

$d=(\omega r+\omega R)\frac{l}{\omega R}$

$l=\left(\frac{r+R}{R}\right)$

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