One end of a light string of length `L` is connected to a ball and the other end is connected to a fixed point `O`. The ball is released from rest at `t = 0` with string horizontal and just taut. The ball then moves in vertical circular path as shown. The time taken by ball to go from position `A` to `B` is `t_(1)` and from `B` to lowest position `C` is `t_(2)`. Let the velocity of ball at `B` is `vec v_(B)` and at `C` is `vec v_(C)` respectively.

If `|vec v_(C)=2|vecv_(B)|` then the value of `theta` as shown is

Options

A. `cos^(-1)((1)/(4))^(1//3)`
B. `sin^(-1)((1)/(4))^(1//3)`
C. `cos^(-1)((1)/(2))^(1//3)`
D. `sin^(-1)((1)/(2))^(1//3)`

Answer

B

Explanation

`V_(C)^(2) +V_(B)^(2) -2V_(C)V_(B) sin theta = V_(B)^(2)`
`rArr V_(C)^(2) = 2V_(C) V_(B) sin theta rArr V_(C) = 2V_(B) sin theta`.