One end of a light of length `L` is connected to a ball and 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 it vertival circular pathh 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 `vecv_(B)` and at `C` is `vecv_(C)` respectively.
If `|vecv_(c)|=2|vecv_(B)|` then

Options

A. `t_(1) gt t_(2)`
B. `t_(1) lt t_(2)`
C. `t_(1) = t_(2)`
D. Information is insufficient.

Answer

B

Explanation

`a = g cos theta` which decreases with time area of `a - t` graph gives change in velocity
`V = sqrt(2gl sin theta) , l (d theta)/(dt) = sqrt(2 gl sin theta)`
`int = sqrt((l)/(2g)) int (d theta)/(sqrt(sin theta)) , t = sqrt((l)/(2g)) int (d theta)/(sqrt(sin theta)) , t_(1) lt t_(2)`.