Acceleration of two drums connected by metal tape

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

For drum A,

Eqn. of COM motion gives,
$T(\hat y ) + Mg (- \hat y ) = M a_A (\hat y )$ ; $a_A = - |a_A|$ eq (1)
I need to know T here for getting $a_A$.

For drum B,
Eqn. of COM motion doesn't give any useful information.
Torque (about COM) analysis gives,
$R(\hat x) \times T ( - \hat y ) = I \alpha_B (\hat z )$ ; $\alpha_B = - | \alpha_B|$ eq (2)

Similar Torque analysis for drum A gives, $\alpha _A = \alpha_B$
Now, the distance the drum A moves down is equal to the sum of the length of the metal ape released by each drum.
This gives, $a_A = ( 2\alpha _B) R$ eq (3)

Now, the above three eqns. give,

$a_A = - \frac 2 3 g,~ g>0$

Is this correct?
Would you please tell me how to number an eqn. on PF?

 

[haruspex]

Is this correct?

Assuming the drums are hollow, yes.
can't help with the equation numbering.