$A$ proton and an $\alpha$-particle enter a uniform magnetic field perpendicularly with the same speed. If a proton takes $25 \ \mu s$ to make $5$ revolutions,then the periodic time for the $\alpha$-particle would be ........ $\mu s$.

$A$ proton moving with a velocity of $8 \times 10^5 \ m/s$ enters a uniform magnetic field normal to the direction of the magnetic field. If the radius of the circular path of the proton in the magnetic field is $8.3 \ cm$,then the magnitude of the magnetic field is (Charge of proton $= 1.6 \times 10^{-19} \ C$ and mass of the proton $= 1.66 \times 10^{-27} \ kg$) (in $mT$)

$A$ proton with a kinetic energy of $2.0 \, eV$ moves into a region of uniform magnetic field of magnitude $\frac{\pi}{2} \times 10^{-3} \, T$. The angle between the direction of magnetic field and velocity of proton is $60^{\circ}$. The pitch of the helical path taken by the proton is $.......... \, cm$. (Take,mass of proton $= 1.6 \times 10^{-27} \, kg$ and charge on proton $= 1.6 \times 10^{-19} \, C$)

$A$ charge moves in a circular path perpendicular to a magnetic field. The time period of the revolution is independent of

$OABC$ is a current-carrying square loop. An electron is projected from the center of the loop along its diagonal $AC$ as shown. The unit vector in the direction of initial acceleration will be

$A$ particle having some charge is projected in the $x-y$ plane with a speed of $5\ m/s$ in a region having a uniform magnetic field along the $z-$ axis. Which of the following cannot be the possible value of velocity at any time?