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A system consists of three masses m₁, m₂ and m₃ connected by a string passing over a pulley P. The mass m₁ hangs freely and m₂ and m₃ are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m₁ is: (Assume m₁ = m₂ = m₃ = m)

1. g(1 - gμ)/g
2. 2gμ/3
3. g(1 - 2μ)/3
4. g(1 - 2μ)/2

Correct answer: g(1 - 2μ)/3

Solution

The forces acting on the system include the weight of m₁, the tension in the string, and the frictional forces on m₂ and m₃. Using Newton's second law and accounting for the frictional forces (2μmg), the net acceleration of the system is derived as g(1 - 2μ)/3.

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