A $10 \;eV$ electron is circulating in a plane at right angles to a uniform field at magnetic induction $10^{-4} \;W b / m^{2}(=1.0$ gauss), the orbital radius of electron is ........ $cm$

Tesla is a unit for measuring

At $t$ = $0$, a positively charged particle of mass $m$ is projected from the origin with velocity $u_0$ at an angle $37^o $ from the $x-$axis as shown in the figure. A constant magnetic field ${\vec B_0} = {B_0}\hat j$  is present in space. After a time interval $t_0$ velocity of particle may be:-

A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. the time spent by the particle in the magnetic field is......$ns$

A proton (mass $m$ and charge $+e$) and an $\alpha  -$ particle (mass $4m$ and charge $+2e$) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true

A charge particle of charge $q$ and mass $m$ is accelerated through a potential diff. $V\, volts$. It enters a region of orthogonal magnetic field $B$. Then radius of its circular path will be