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) $\operatorname{Tr}=\frac{ mr ^2}{2} \alpha_1$.......(i)
$Tr =\frac{ mr ^2}{2} \alpha$............(ii)
$\alpha_1=\alpha^2$....(iii)
Acceleration of point $b=$ acceleration of point $a$
$r \alpha_1=a_{c m}-r \alpha$............. (iv)
Hence, $2 r \alpha= a _{ cm }$