A body initially at rest sliding along a frictionaless track 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

As body is at rest initially, i.e., speed = 0
At point A, speed = v,
As track is frictionless , so total mechanical energy will remain constant
`:. (T.M.E)_(i) = (T.M.E)_f`
`0 mgh = 1/2 mv^2 + 0 " or " h = (v^2)/(2g)`
For completing the vertical circle, `v ge sqrt(5 gR)`
`:. h = (5 gR)/(2g) = 5/2 R = 5/4 D`