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A sphere is rolling down a rough inclined plane. At any instant if R be the normal reaction on it and F be the frictional force along the plane (μ\muμ
Question

A sphere is rolling down a rough inclined plane. At any instant if R be the normal reaction on it and F be the frictional force along the plane (μ\mu = coefficient of friction) then for limiting equilibrium,

A.

F>μRF > \mu R​​

B.

F<μRF < \mu R​​

C.

F=μRF = \mu R​​

D.

nothing can be said.

Correct option is C

Solution:
When a body rolls down an inclined plane, static friction acts to prevent slipping.
The maximum possible static friction is given by μR, where μ is the coefficient of friction and R is the normal reaction.
Limiting equilibrium refers to the condition where the object is just on the verge of slipping. In this case, the static friction has reached its maximum possible value.
So, in limiting equilibrium:

F = μR

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