Question

Two identical uniform 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 among $a_{cm}$, $\alpha$ and $r$ is

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

Answer 1

Answer: (B)

$a_{cm}=2\alpha r$

When the lower disc has an angluar acceleration of $\alpha$ the upper disc also accelerates at $\alpha$, they being identical and the tension on rope is same for both discs

$\alpha =\frac{\partial \omega }{\partial t}$

$a_{cm}=\frac{\partial r\omega }{\partial t}+\frac{\partial r\omega }{\partial t}=2r\alpha$

Answer. B