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
$1: \sqrt{2}: \sqrt{2}$
$1: 1: \sqrt{2}$
$\sqrt{2}: 1: 1$
$1: \sqrt{2}: 1$
${H^ + },\,H{e^ + }$ and ${O^{ + + }}$ ions having same kinetic energy pass through a region of space filled with uniform magnetic field $B$ directed perpendicular to the velocity of ions. The masses of the ions ${H^ + },\,H{e^ + }$and ${O^{ + + }}$ are respectively in the ratio $1:4:16$. As a result
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 proton of velocity $\left( {3\hat i + 2\hat j} \right)\,ms^{-1}$ enters a magnetic field of $(2\hat j + 3\hat k)\, tesla$. The acceleration produced in the proton is (charge to mass ratio of proton $= 0.96 \times10^8\,Ckg^{-1}$)
Maximum kinetic energy of the positive ion in the cyclotron is
Two ions of masses $4 \,{amu}$ and $16\, amu$ have charges $+2 {e}$ and $+3 {e}$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :