Two masses M1=5kg and M2=10kg are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When the masses are released, then the acceleration of the masses will be:

Let the acceleration of the blocks and the tension in the string be a and T respectively.
For block of mass M1: M1a = T - M1g (1)
For block of mass M2: M2a = M2g - T (2)
Adding (1) and (2) we get
(M1+M2)a = (M2 - M1)g ⇒ a = (M2 - M1)/(M2 + M1)g
Given : M1 = 5kg M2 = 10kg
a = (10 - 5)/(10 + 5)g ⇒ a = g/3