Two particles, each of mass m and charge q, are attached to the ends of a light rigid rod of length 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)`