Question

Two particles , each of mass ` m` and charge `q`, are attached to the two ends of a light rigid rod of length ` 2 R` . 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. `(q)/(2m)`
B. `(q)/(m)`
C. `(2q)/(m)`
D. `(q)/( pi m)`

Answer 1

Correct Answer - A
Current , `I = (frequency) (charge) = ((omega)/( 2 pi)) (2 q) = (q omega)/( pi) `
Magnetic moment,
` M = (i)(A) = ((q omega)/( pi)) ( pi R^(2)) = ( q omega R^(2))`
Angular momentum , ` L = 2 Iomega = 2 (mR^(2))omega`
` (M)/(L) = ( q omegaR^(2))/(2 (mR^(2))omega = (q)/( 2m)`