Consider a quarter circular smooth rod AB fixed AB fixed in a vertical plane with centre of the circle at O. A bead of mass m slides without friction with the help of string starting from point A under the action of a constant force `F = 2 gm` as shown in figure.

The velocity of bead when string makes an angle `30^(@)` with the horizontal is nearly :

Options

A. `sqrt(g R (4 sqrt2 - 5))`
B. `2 sqrt(gR)`
C. `sqrt(g R (5 - 2 sqrt3))`
D. `5 sqrt (gR)`

Answer

A

Explanation

`theta = 30^(@)`
`Delta POB` becomes an equilateral `Delta`
WET,
`W_(g) + W_(T) + W_(N) = DeltaK`
`- mg R sin theta + (2 mg) [sqrt2 R - R] + 0 = (1)/(2)`
`mv^(2) - 0`