Question

Two identical discs of mass $m$ and radius $r$ are arranged as shown in the figure. If $\alpha$ is the angular acceleration of the lower disc and $a_{cm}$ is acceleration of centre of mass of the lower disc, then relation between $a_{cm},\alpha$ and $r$ is

• A. $a_{cm}=\alpha /r$
• B. $a_{cm}=2\alpha r$
• C. $a_{cm}=\alpha r$
• D. None of these

Answer 1

Answer: (B)

(b) $\mathrm{Tr}=\frac{m{r}^2}{2}{\alpha }_1$.......(i)
$Tr=\frac{m{r}^2}{2}\alpha$............(ii)
${\alpha }_1={\alpha }^2$....(iii)
Acceleration of point $b=$ acceleration of point $a$
$r{\alpha }_1=a_{cm}-r\alpha$............. (iv)
Hence, $2r\alpha =a_{cm}$