The pulleys and strings shown in the figure are smooth and negligible mass. For the system to remain in equilibrium the angle $\theta$ should be_______ in degrees  

For block a A, $T-mg=m\left(0\right)$

For block a B, $T-mg=m\left(0\right)$

(Since the both A and B blocks are similar and tension in the strings are mg. It has zero acceleration, as system is in equilibrium)

So, $2T\cos \theta =\sqrt{2}mg$

$2mg\cos \theta =\sqrt{2}mg$

 $\theta ={45}^{\circ }$