Question

two weights w1 and w2 are suspended from the ends of a light string passing over a smooth fixed pulley . if the pulley is pulled up at an acceleration g, the tension in the string will be..

Answer 1

Since pulley is pushed up with an acceleration equal to g then we can assume that the two blocks are stationary for a time dt with respect to the pulley.
Or R(reaction)-(w1+w2)=2/g(w1+w2)
=>2T=(w1+w2)(2/g+1)=>T=[(w1+w2)(2/g+1)]/2 N.