Two masses A and B having mass m1 = 1 kg and m2= 2 kg are placed on a rough horizontal plane and connected to a string. B is connected to another string which passes over a massless frictionless pulley and connected to a mass m3. Calculate I) the minimum value of m3 required to move the blocks. ii) The value of T1 and T2 when m3 = 1 kg. Coefficient of friction is 0.1.
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m2 m2g- T = m2 a
T- m1g = m1a
Solving these equations we get, a= g/3
Distance travelled by each block
S = ut + (1/2)at^2 = 20/3 m
Applying centre of mass formula
(m2 x s – m1 x s)/(m2 + m1) = 20/9
Hence the ratio between the masses is 20/9.
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