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 $$(Assume$$ $$m1=m2=m3=m$$

Question

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  $$(Assume$$ $$m1=m2=m3=m$$

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Force of friction on mass $$m2=$$μ$$m2g$$        Force of friction on mass     $$m3=$$μ$$m3g$$        Let α be common acceleration of the system.∴ $$a=m1g$$−μ$$m2g$$−μ$$m3gm1+m2+m3$$ Here, $$m1=m2=m3=m$$ Hence, the downward acceleration of mass $$m1$$ is $$g(1$$−$$2$$μ$$)3$$

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