Diagram shows the various forces acting on the masses and their resolution in the direction of motion. Let us consider the two masses to be a system. The forces trying to move the system such that A moves upwards and B moves downwards =‌‌
2mg
√2
−‌‌
mg
√2
=‌‌
mg
√2
The forces trying to stop this motion (i.e., maximum frictional force) =fA+fB=µANA+µBNB
=‌‌
2
3
×‌‌
mg
√2
+‌‌
1
3
×‌‌
2mg
√2
=‌‌
4
3
‌‌
mg
√2
Since the stopping force is more therefore the mass system will not move ⇒ acceleration of the system is zero.