An electron (mass $= 9 \times 10^{-31}\,kg$. Charge $= 1.6 \times 10^{-19}\,C$) whose kinetic energy is $7.2 \times 10^{-18}$ $joule$ is moving in a circular orbit in a magnetic field of $9 \times 10^{-5} \,weber/m^2$. The radius of the orbit is.....$cm$

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

A particle with charge $q$, moving with a momentum $p$, enters a uniform magnetic field normally. The magnetic field has magnitude $B$ and is confined to a region of width $d$, where $d < \frac{p}{{Bq}}$, The particle is deflected by an angle $\theta $ in crossing the field

An electric field of $1500\, V/m$ and a magnetic field of $0.40\, weber/metre^2$ act on  a moving electron. The minimum uniform speed along a straight line the electron could  have is

Two particles $\mathrm{X}$ and $\mathrm{Y}$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $\mathrm{X}$ and $\mathrm{Y}$ is :

A proton, a deuteron and an $\alpha-$particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is