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Question

A system consists of three identical 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
312752.png

A
g(1gμ)9
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B
2gμ3
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C
g(12μ)3
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D
g(12μ)2
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Solution

The correct option is D g(12μ)3
For the motion of horizontal block, (m2+m3)a=Tf2f3
or (m+m)a=Tμmgμmg
or 2ma=T2μmg....(1)
For the motion of vertical block, m1a=m1gT or ma=mgT...(2)
From (1) and (2), 2ma=mgma2μmg
or 3a=g2μg
or a=g(12μ)3

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