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

(A)  tanθ = 1 + 2 M m           (B)  tanθ = 1 + 2 m M            (C)  tanθ = 1 + M 2 m          (D)  tanθ = 1 + m 2 M

Dear Student, 

Firstly find the all the forces acts on a first junction,
resolve all the inclined force, mg act downward and Tand Tresolved.
we can write,

Free body diagram for mass M
 Fx=0T3cosθ=T1cos45o-----iiiFy=0T3sinθ=T1sin45o+Mg----ivdivide equation iv by iiitanθ=T1sin45o+MgT1cos45o=mg/2+Mgmg/2= 1+2Mm
so, option (a) is correct

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