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# A system consists of three masses   connected by a string passing over a pulley P. The mass ${m}_{1}$ hangs freely and ${m}_{2}$ and ${m}_{3}$ are on a rough horizontal table (the coefficient of friction= $\mu$)The pulley is frictionless and of negligible mass. The downward acceleration of mass ${m}_{1}$ is

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a
g(1−gμ)9
b
2gμ3
c
g(1−2μ)3
d
g(1−2μ)2
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detailed solution

Correct option is C

Force of friction on mass m2=μm2g        Force of friction on mass     m3=μm3g        Let α be common acceleration of the system.∴ a=m1g−μm2g−μm3gm1+m2+m3 Here, m1=m2=m3=m Hence, the downward acceleration of mass m1 is g(1−2μ)3

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A skier starts from rest at point A and slides down the hill without turning or breaking. The friction coefficient is $\mu$. When he stops at point B, his horizontal displacement is s. What is the height difference between points A and B

(The velocity of the skier is small, so that the additional pressure on the snow due to the curvature
can be neglected. Neglect also the friction of air and the dependence of $\mu$ on the velocity of the skier.)

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