A body initially rest and sliding along a frictionless trick from a height `h` (as shown in the figure) just completes a vertical circle of diameter `AB = D`. The height `h` is equal to

Options

A. `(5)/(4) D`
B. `(3)/(2) D`
C. `(7)/(5) D`
D. `D`

Explanation

For completing the vertical circle the minimum velocity of the body at `B` should be `sqrt(5gR)`, where
`R = (D)/(2)`
Hence, `v_(A) = sqrt((5)/(2)gD)`
Now applying C.O.M.E. between `O and A`.

`Delta K+ DeltaU = 0 implies ((1)/(2) mv_(A)^(2) -0) - mgh = 0`
`(1)/(2) m (5)/(2) gD = mgh or h = (5)/(4) D`