A partical originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance `h` below the highest points, such that `h` is equal to

Options

A. `R`
B. `R//4`
C. `R//2`
D. `R//3`

Answer

D

Explanation

`h = R - R cos theta: v = sqrt(2gh) = sqrt(2gR(1 - cos theta))`
`mg cos theta - N = mv^(2)//R`
when it leavels circule : `N = 0`
`mg cos theta = (mv^(2))/(g) implies cos theta = (2)/(3)`
h = R-R cos theta = R//3`