A bob attached to one end of a string, other end of which is fixed at peg `A`. The bob is taken to a position where string makes an angle of to a position where string makes an angle of `30^@` with the horizontal. On the circular path of the bob in vertical plane there is a ped 'B' at a symmetrical position with respect to the position of release as shown in the figure. If `V_(c)` and `V_(a)` be the minimum speeds is clockwise and anticlock wise directions respectively, given to the bob in order to hit the ped 'B' then ratio `V_(c) : V_(a)` is equal to
.

Options

A. `1 : 1`
B. ` 1: sqrt(2)`
C. `1 : 2`
D. `1 : 4`

Answer

C

Explanation

For complete circular motion speed at highest point in `sqrt(gR)`
Applying conservation energy `v_(a) = sqrt(2gR)`
For clock wise motion
`T +mg cos 60 = (mv_(c)^(2))/(R)`
`v_(C)` to minimum `T=0 , v_(C) = sqrt((gR)/(2))`.