Question

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. $\frac{q}{\pi m}$

Answer 1

The correct option is A $\frac{q}{2m}$


$i=\frac{2q\omega }{2\pi }=\frac{q\omega }{\pi }$; $\therefore M=iA=\frac{q\omega }{\pi }\pi r^2=q\omega R^2$
$L=2R.mv=2RmR\omega =2m{R}^2\omega$ $(\because v=R\omega )$
$\Rightarrow \frac{M}{L}=\frac{q}{2m}$