A copper wire `ab` of length `l`, resistance `r` and mass `m` starts sliding at `t=0` down a smooth, vertical, thick pair of connected condcuting rails as shown in figure.A uniform magnetic field `B` exists in the space in a direction perpendicular to the plane of the rails which options are correct.

Options

A. The magnitude and direction of the induced current in the wire when speed of the wire v is `(vBl)/( r)`, a to b
B. The downward acceleration of the wire at this instant `g-(B_(2)l^(2))/(mr)v`
C. The velocity of the wire as a function of time `v_(m)(1-e^(-"gt"//v_(m))),("where" v_(m)=(mgr)/(B^(2)l^(2)))`
D. The displacement of the wire as a function of time `v_(m)t-(v_(m)^(2))/(g)(1-e^(-"gt"//v_(m))),("where" v_(m)=(mgr)/(B^(2)l^(2)))`

Answer

A, B, C, D