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  • A small block starts slipping down from a point B on an inclined plane AB, which is making an angle

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 ___________  
Option: 1 1
Option: 2 2
Option: 3 3
Option: 4 4

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\begin{aligned} &\text { from work energy theorem }\\ &W_{g}+W_{f}=\Delta K E\\ &\operatorname({mg}\sin \theta* 3x) -(\mu \operatorname{mgcos} \theta* x)=0-0\\ &3 \tan \theta=\mu\\ &K=3 \end{aligned}

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