A thin conducting rod of length 1 is moved such that its end \( B \) moves along the \( X \)-axi...

A thin conducting rod of length 1 is moved such that its end \( B \) moves along the \( X \)-axis while end \( A \) moves along the \( Y \)-axis. A uniform magnetic field \( B=B_{0} \hat{k} \) exists in the region. At some instant, velocity of end \( B \) is \( v \) and the rod makes an angle of \( \theta=60^{\circ} \) with the \( X \)-axis as shown in the figure. Then, at this instant
(a) Angular speed of \( \operatorname{rod} A B \) is \( \omega=\frac{2 v}{\sqrt{3} l} \)
(b) Angular speed of \( \operatorname{rod} A B \) is \( \omega=\frac{\sqrt{3} v}{2 l} \)
(c) E.M.F. induced in \( \operatorname{rod} A B \) is \( B l v \sqrt{3} \)
(d) E.M.F. induced in \( \operatorname{rod} A B \) is \( B l v / 2 \sqrt{3} \)