KVPY Sample Paper KVPY Stream-SX Model Paper-22

A thin uniform ring of radius \[R\] carrying uniform charge \[Q\] and mass \[M\] rotates about its axis with angular velocity \[\omega \]. The ratio of its magnetic moment and angular momentum is:

A) \[\frac{Q}{M}\]

B) \[\frac{M}{Q}\]

C) \[\frac{Q}{2M}\]

D) \[\frac{M}{2Q}\]

Correct Answer: C

Solution :

\[M=iA=\frac{Q}{T}A=\frac{Q\omega }{2\pi }\times \pi {{R}^{2}}=\frac{Q\omega {{R}^{2}}}{2}\]

\[L=I\omega =M{{R}^{2}}\omega \]

\[\therefore \] \[\frac{M}{L}=\frac{Q\omega {{R}^{2}}/2}{M{{R}^{2}}\omega }=\frac{Q}{2M}.\]