Under the influence of a uniform magnetic field a charged particle...

When magnetic field is perpendicular to motion of charged particle, then Centripetal force = magnetic force ie, $\frac{m v^2}{R}=B q v$ or $R=\frac{m v}{B q}$ Further, time period of the motion or $T=\frac{2 \pi R}{v}=\frac{2 \pi\left(\frac{m v}{B q}\right)}{v} or$\quad T=\frac{2 \pi m}{B q}$It is independent of both$R and $v$.