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.

Options

A. `sqrt((27)/(7)g(R - r))`
B. `sqrt((20)/(7)g(R - r))`
C. `sqrt((20)/(7)g R)`
D. `sqrt((17)/(7) g(R - r))`

Answer

A

Explanation

(a) `KE` of sphere `= (7)/(10) mv^2`
`(7)/(10) mv'^2 + mg 2 (R - r) = (7)/(10) mv^2`
but `v'_(min) = sqrt(g(R - r))`
Put the value of `v'` and solve to
get `v = sqrt((27)/(7) g (R - r))`.
.