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Questions  

The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the Lower half is given by
 

a
2sin⁡ϕ
b
2cos⁡ϕ
c
2tan⁡ϕ
d
tan⁡ϕ

detailed solution

Correct option is C

According to work energy theoremW=Δk=0 (∵ Initial and final speeds are zero ) ∴  Work done by friction + Work done by gravity =0  or −(μmgcos⁡ϕ)l2+mglsin⁡ϕ=0 μ2cos⁡ϕ=sin⁡ϕ

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The curved portions are smooth and horizontal surface is rough. The block is released from P. At what distance from A, it will stop (if μ = 0.8)?


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