A force F is applied on block A of mass M so that the tension in light string also becomes F when block B of mass m acquires an equilibrium state with respect to block A. find the force F. Give your answer in terms of m, M and g.

Explanation

Applying newton's law on the system in horizontal direction`F=(M+m)a`.
Now consider the equilibrium
of block B w.r.t. block M
`F^2=(mg)^2=(m(F)/(m+M))^2`
`F^2=(m^2g^2)/(1-(m^2)/((m+M)^2))`,`F=(mg)/(sqrt(1-((m)/(m+M))^2))`