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Question

Masses M1,M2 and M3 are connected by strings of negligible mass which pass over massless and frictionless pulleys P1 and P2 as shown in fig. The masses move such that the portion of the string between P1 and P2 is parallel to the inclined plane and the portion of the string between P2 and M3 is horizontal. The masses M2 and M3 are 4.0 kg each and the coefficient of kinetic friction between the masses and the surface is 0.25. The inclined plane makes an angle of 37 with the horizontal. If the mass M1 moves downwards with a uniform velocity. find the mass of M1 in kg.

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Solution

For M1 to move with uniform velocity net acceleration must be zero. So,M1g=μM2gcosθ+μM3g+M2gsinθ
M1=μ(M2cosθ+M3)+M2sinθ
=0.25((4)45+4)+(4)35=215=4.2kg

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