Figure shows a rod AB that can rotate with uniform angular velocity $ω$ over a stationary conducting circular frame and resistance R is connected between centre A and frame.

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If the current was found to be I then the charge to mass ratio of electrons would be $\frac{ω^{2} l^{2}}{2 I R}$

If the current was found to be I then the charge to mass ratio of electrons would be $\frac{2 ω^{2} l^{2}}{I R}$

If a magnetic field B is applied perpendicular to plane of the paper then induced current in rod will be radially outward

If a magnetic field B is applied perpendicular to plane of the paper then induced current (due to
motional emf only) in rod will be $\frac{1}{2} \frac{B l^{2} ω}{R}$

answer is A, C.

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Detailed Solution

Due to centrifugal force electrons are moving from A to B. At equilibrium, Electric force due to induce charges become equal to centrifugal force $m ω^{2} x = e E$
$\int_{0}^{l} m ω^{2} x d x = \int_{0}^{l} e E d x = e \int_{0}^{l} E d x \Rightarrow \frac{m ω^{2} l^{2}}{2} = e v (v = v o l t a g e a c r o s s r o d) \Rightarrow v = i R = \frac{m ω^{2} l^{2}}{2 e} \Rightarrow \frac{e}{m} = \frac{ω^{2} l^{2}}{2 i R}$

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