question_answer

Two particles each of mass m and charge g are attached to the two ends of a light rigid rod of length \[2l\]. The rod is rotated at constant   angualr 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)  \[\frac{q}{\pi m}\]                         

B)  \[\frac{q}{m}\]   

C)  \[\frac{2q}{m}\]                             

D)  \[\frac{q}{2m}\]

Correct Answer: D

Solution :

                 We know that                 \[L=l\omega \]                 \[L=2\,{{m}^{2}}\times \omega \]                                            ?. (i) and        \[m=lA\]                 \[=\frac{q}{T}.A\]                 \[=2q\times f\,\pi {{l}^{2}}\]                 \[=2q\times \frac{\omega }{2\,\pi }\times \pi r{{l}^{2}}\]                 \[=q\omega {{l}^{2}}\]                                                  ?. (ii) From Eqs. (ii) and (ii), we get                 \[\frac{m}{L}=\frac{q{{\omega }^{2}}}{2{{m}^{2}}\times \omega }=q/2m\]