Two masses are connected by a string which passes over a pulley accelerating upward at a rate A shown. If a1 and a2 be the accelerations of bodies I and 2 respectively then,

Since length of the string is constant. So,(YP-y1) + πR + (Yp-y2) = constant. So,Take second derivative of both sides twice w.r.t. time t,   We get ,(A-a1)+0+[A--a2]=0 ⇒A=a1-a22