The net torque about a point is,
\(T_{net} = I\alpha\)
Where \(I\) is the moment of inertia and α is the angular acceleration.
The net torque of the upper disc of mass \(m\) and radius \(r\) is,
\(Tr = \frac{mr^2}{2} \alpha_1 \quad....(i)\)
For the lower disc,
\(Tr = \frac{mr^2}{2} \alpha \quad....(ii)\)
From (i) and (ii),
\(\alpha_1 = \alpha \quad....(iii)\)
As the string does not get slack,
Acceleration of point A is equal to the acceleration of point B.
\(r\alpha_1 = a_{cm} - r\alpha\)
From equation (iii),
\(a_{cm} = 2r\alpha\)
