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A force F is applied on block A of mass ...


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.

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A, B
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
Applying Newton's law on the system in horizontal direction `F=(M+m)a`.
Now consider the equlibrium of block `B w.r.t.` block `M`

`F^(2)=(mg)^(2)+(ma)^(2)+(m(F)/(m+M))^(2)`
`:. F^(2)=(m^(2)g^(2))/(1-(m^(2))/((m+M)^(2))),`
`F=(mg)/(sqrt(1-((m)/(m+M))^(2)))`
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