The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.
We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.
Στ(B) = 0
τ(a) + τ(b) + τ(m1) + τ(m2) = 0
τ = r×F×sin(θ)
d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0
d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0
Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d
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