Two masses m and M are attached with strings.for the system to be in equilibrium we have

We regard first M and m forming a single system. Then,applying Newton’s second law,we have
(M+m) a=F ……………(1) Let F be applied on M. From free body diagram of M we have following equation.
Ma=F-T………………….(2) Therefore,T=F-Ma .Substituting for a from Eq.(1),we get,
T=F-M(F/M+m)=Fm/M+m…………(3).
This tension is the force on m. Then, writing Eq. Of motion for m,
ma=T=Fm/(M+m). But if we assume the force F applied on m then the tension will be T=FM/(M+m).