Question

The lower half of an inclined plane is rough the upper half being smooth a particle is allowed to slide from the top and is brought to rest by friction just as it reaches the bottom, find the ratio of the force of friction to the weight of the particle intermes of the coefficient of friction.
at rest so no net force
force down plane = m g sin T
force up plane = mu m g cos T
so
m g sin T = mu m g cos T
so
mu = tan T if friction just holds it

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