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A sphere of radius a rests on top of a fixed rough circular cylinder of radius R which is lying with its principal axis horizontal. The sphere is disturbed and rolls, without any slipping, around the surface of the cylinder. Show from energy considerations that, if theta is the angle to the vertical made by the line joining the centre of the sphere directly to the axis of the cylinder, then

(w)^2 = [10g(1 - cos theta)] / [7(R+a)]

where (w)^2=angular velocity squared, g=acceleration due to gravity

Hence, show that the sphere will leave the surfacve of the cylinder at

theta = arccos (10/17)

(w)^2 = [10g(1 - cos theta)] / [7(R+a)]

where (w)^2=angular velocity squared, g=acceleration due to gravity

Hence, show that the sphere will leave the surfacve of the cylinder at

theta = arccos (10/17)

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