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. `3/2 D`
B. D
C. `7/5 D`
D. `5/4 D`

Answer

D

Explanation

To complete a vertical circle, speed at A should be
`V_(A) = sqrt(5gR)`
using energy conservation.
`mgh = 1/2 mv_(A)^(2)`
`h = 1/2 v_(A)^(2)/g =1/2 (5g)/g.D/2 (R =D/2)`
`= (5D)/4`