In the arrangement shown in the figure, the acceleration of the pulley is, (Ignore friction and mass of the pulley).

Constraint equation xp + (xp – xM) = L = length of the string ⇒ 2xp - xM = Ldifferentiating twice with respect to time, we get 2ap – aM = 0ap=aM2aM=F2M ⇒ap=F4M