A conducting rod of length \( l \) is moved at constant velocity \( v_{0} \) on two parallel, co...

A conducting rod of length \( l \) is moved at constant velocity \( v_{0} \) on two parallel, conducting, smooth, and fixed rails, that are placed in a uniform constant magnetic field \( B \) perpendicular to the plane of the rails as shown in the below figure. A resistance \( R \) is connected between the two ends of the rail. Then, which of the following is/are correct?
(A) The thermal power dissipated in the resistor is equal to rate of work done by external.
(B) If applied external force is doubled than a part of external power increases the velocity of rod.
(C) Lenz's law is not satisfied if the rod is accelerated b external force.
(D) If resistance \( R \) is doubled then power required to maintain the constant velocity \( v_{0} \) becomes half.