A smooth track in the form of a quarter circle of radius `6 m` lies in the vertical plane. A particle moves from `P_(1)` to `P_(2)` under the action of forces `vec F_(1),vecF_(2)` and `vec F_(3)` Force `vec F_(1)` is always `30 N` in magnitude. Force `vec F_(3)` always acts tangentiallly to the track and is of magnitude `15 N`. Select the correct alternative (s) :
.

Options

A. Work done by `F_(1)` is 120 J
B. Work done by `F_(2)` is 180 J
C. Work done by `F_(3)` is `45 pi`
D. `F_(1)` is conservative in nature

Answer

B, C, D