Force due to 5kg block = 5g downwards

.: torque of this force about center = 5g * (1/2) (clockwise)

&torque due to 2kg block = g (anticlockwise)

Net torque at the center = 5g/2-g=3g/2

Moment of inertia of the system about center = moi of 5kg + moi of 2kg

= 5*(1/2)² + 2(1/2)

= 5/4+2/4 = 7/4

Net torque = I

3g/2 = 7/4 * ()

.:  = 8.4 rad/sec