Figure shows a rough track a portion of which is in the form of a cylinder of radius R. With what minimum linear speed should as sphere of radius r be set rolling on the horizontal part so that it completely goes round the circle on the cylindrical part.

Answer

B

Explanation

At the topmost point, `(mv^2)/((R_r))=g`
`rarr v^2=g(R-r)`
Let the spehre is thrown with velocity v therefore applying laws of conservation of energy.
`rarr 1/2mv'^2+1.2Iomega^2`
`mg^2(R-r)+1/2mv^2+1/2Iomega^2`
`rarr 7/10v'^2=g^2(R-r)+7/10v^2`
`=v'^2=20/g(R-r)+g(R-r)`
`rarrv'^2=27/7g(R-r)`
`rarr v'=sqrt({27/7}g(R-r))`