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  4. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-vnlv0ohemxflxqiu.jpg /> A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction μ . It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC=2AC, the coefficient of friction is given by μ =k tan θ . The value of k is

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Q. Question
A small block starts slipping down from a point $B$ on an inclined plane $AB,$ which is making an angle $\theta $ with the horizontal section $BC$ is smooth and the remaining section $CA$ is rough with a coefficient of friction $\mu .$ It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $BC=2AC,$ the coefficient of friction is given by $\mu =k\tan \theta .$ The value of $k$ is

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
from work energy theorem
$W_{g}+W_{f}=\Delta kE$
$mg 3x \sin\theta -\mu mg\cos\theta x=0-0$
$\Rightarrow mg 3x\sin\theta =\mu mg\cos \theta x$
$3\tan \theta =\mu $
$k=3$