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Let
T = tension in the string connected to m1,
a1 = acceleration of mass m1
a2 = acceleration of mass m2
Then from constraint equation for the string, we can write a1 = 2a2 eq(1).
From free body diagram for m1, T = m1a1 eq(2).
From free body diagram for m2, F – 2T = m2a2 eq(3)
Solving above equations, we get
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