c
\(\text { Frequency, } v=\frac{e B}{2 \pi m}\)

or \(\quad B=\frac{2 \pi m v}{e}.........(i)\)

As \(\frac{m v^{2}}{R}=e v B\)

\({\text{or }}v = \frac{{eBR}}{m} = \frac{{e2\pi mvR}}{{me}}\,\,\,\,\,(U\sin g\,(i))\)

\( = 2\pi vR{\text{ }}.........{\text{(ii)}}\)

\({\text{Kinetic energy, }}K = \frac{1}{2}m{v^2} = \frac{1}{2}m{(2\pi vR)^2}{\text{ }}\)

\(=2m\pi ^2v^2R^2\)