Two particles, each of mass mand charge q, are attached to the two ends of a light rigid rod oflength 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its center. The ratio of the magnitudes of the moment of the system and its angular momentum about the center of the rod is

Options

A. `q/(2m)`
B. `q/m`
C. `(2q)/m`
D. `q/(pim)`

Answer

A

Explanation

Current `i` = (frequency) (charge) `=(omega/(2pi))(2q)=(qomega)/pi`

Magnetic moment, `M=(I)(A)=((qomega)/pi)(piR^2)=(qomegaR^2)`
Angular momentum, `L=2Iomega=2(mR^2)omega`
`M/L=(qomegaR^2)/(2(mR^2)omega)=q/(2m)`