A bead slides on a fixed frictionless wire bent into a horizontal semicircle of radius `R_(0)` as shown in figure. In addition to any normal forces exerted by the wire, the bead is subjected to an external force that points directly away from origin and depends on distance r from the origin according to the formula `F=F_(0)((r )/(R_(0)))^(2)hat(r)`

Options

A. Given force is a central force
B. Given force is a conservation force
C. Work done by external force as bead leaves the track (starting from origin) is `(8F_(0)R_(0))/(3)`
D. Speed v of bead as it leaves the wire at P is `sqrt(v_(0)^(2)+(18F_(0)R_(0))/(3m))`

Answer

A, B, C