Two particles each of mass $m$ and charge $q$ are attached to the two ends of a light rigid rod of length $2R$. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is
A$\frac{q}{{2m}}$
B$\frac{q}{m}$
C$\frac{{2q}}{m}$
D$\frac{q}{{\pi m}}$
IIT 1998, Diffcult
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A$\frac{q}{{2m}}$
a (a) $i = \frac{{2q\omega }}{{2\pi }} = \frac{{q\omega }}{\pi };\;\;\therefore M = iA = \frac{{q\omega }}{\pi }\pi {R^2} = q\omega {R^2}$
$L = 2R.mv = 2R.mR\omega = 2m{R^2}\omega \;\;(\therefore v = R\omega )$
$==>$ $\frac{M}{L} = \frac{q}{{2m}}$
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