A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The direction of the frictionless force acting on the cylinders is ___________

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A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The direction of the frictionless force acting on the cylinders is ___________

(a) Up the incline, while ascending and down the incline, while descending

(b) Up the incline, while ascending as well as descending

(c) Down the incline, while ascending and up the incline, while descending

(d) Down the incline, while ascending as well as descending

I got this question by my college professor while I was bunking the class.

Query is from Significance of Moment of Inertia topic in division Laws of Motion of Engineering Physics I

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Right answer is (b) Up the incline, while ascending as well as descending

To explain I would say: Whether the cylinder rolled up or down, the centre of mass and hence the point of contact of the cylinder has an acceleration g sinθ in the downward direction. Hence in both cases, the force of friction acts up the inclined plane.

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