$A$ proton carrying $1\, MeV$ kinetic energy is moving in a circular path of radius $R$ in a uniform magnetic field. What should be the energy of an $\alpha$-particle to describe a circle of the same radius in the same field? ........$MeV$

Two particles $X$ and $Y$ having equal charges,are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii $r_1$ and $r_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is

An electron and a proton have equal kinetic energies. They enter a magnetic field perpendicularly. Then:

For a positively charged particle moving in a $x-y$ plane initially along the $x$-axis,there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond $P$. The curved path is shown in the $x-y$ plane and is found to be non-circular. Which one of the following combinations is possible?

${O^{++}}, {C^+}, {He^{++}}$ and ${H^+}$ ions are projected on a photographic plate with the same velocity in a mass spectrograph. Which one will strike the farthest?

$A$ proton and an $\alpha$-particle (with their masses in the ratio of $1:4$ and charges in the ratio of $1:2$) are accelerated from rest through a potential difference $V$. If a uniform magnetic field $B$ is set up perpendicular to their velocities,the ratio of the radii $r_p : r_{\alpha}$ of the circular paths described by them will be