Two parallel resistance less rails are connected by an inductor of inductance L at one end as shown in the figure. A magnetic field B exists in the space which is perpendicular to the plane of the rails. Now a conductor of length l and mass m is placed transverse on the rails and given an impulse J towards the rightward direction. Then choose the correct option.

Velocity of the conductor is half of the initial velocity after a displacement of the conductor,  $d=\sqrt{\frac{3J^{2}L}{4B^2{\mathcal{l}}^{2}m}}$

Current flowing through the inductor at the instant when velocity of the conductor is half of the initial velocity is  $i=\sqrt{\frac{3J^2}{2Lm}}$

Velocity of the conductor is half of the initial velocity after a displacement of the conductor,  $d=\sqrt{\frac{3J^{2}L}{B^2{\mathcal{l}}^{2}m}}$

Current flowing through the inductor at the instant when velocity of the conductor is half of the initial velocity is $i=\sqrt{\frac{3J^2}{Lm}}$