A small body A starts sliding from the height h down an inclined groove passing into a half-circle of radius `h//2` (figure).

Assuming the friction to be negligible, find the velocity of the body at the highest point of its trajectory (after breaking off the groove).

Options

A. `sqrt((9)/(27) gh)`
B. `sqrt((8)/(27) gh)`
C. `sqrt((27)/(8)gh)`
D. `sqrt((10)/(27)gh)`

Answer

B

Explanation

`v^(2)` (at end of track) `= 2gh`
Let body break at angle `theta` the `(m u^(2))/((h)/(2)) = mg cos theta`…(1)

`u^(2)=v^(2)-2g "h/(2)(1+cos theta)`
solving `cos theta = (2)/(3)` & `u = sqrt((2)/(3)gh)`
`v` at highest `Pt` is
`u cos theta = sqrt((2)/(3)) gh xx (2)/(3) = sqrt((8)/(27)gh)`.