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Figure shows a rough track, a portion of which is in the form of a cylinder of radius R. With what minimum velocity a sphere of radius r be set rolling on the horizontal part so that it completely goes around the circle on the cylindrical part?

a
277g(R-r)
b
207g(R-r)
c
207gR
d
177g(R-r)

detailed solution

Correct option is A

KE of sphere = 710mv2    710mv'2 +mg2(R-r) = 710mv2but vmin' = g(R-r)put the value of v' and solve toget v = 277g(R-r)

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