An $\alpha$-particle (mass $4 amu$ ) and a singly charged sulfur ion (mass $32 amu$ ) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_\alpha$ and $r_5$, respectively. The ratio $\left(r_s / r_\alpha\right)$ is. . . . .$(4)$

A particle of specific charge $(q/m)$ is projected from the origin of coordinates with initial velocity $[ui - vj]$. Uniform electric magnetic fields exist in the region along the $+y$ direction, of magnitude $E$ and $B.$ The particle will definitely return to the origin once if

A charged particle is moving in a uniform magnetic field in a circular path. Radius of circular path is $R$. When energy of particle is doubled, then new radius will be

Which of the following particle will describe the smallest circle when projected with the same  velocity perpendicular to the magnetic field ?

A charged particle of charge $\mathrm{e}$ and mass $\mathrm{m}$ is moving in an electric field ${{\rm{\vec E}}}$ and magnetic field ${{\rm{\vec B}}}$ Construct dimensionless quantities and quantities of dimension [T]-1

A car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a fictionless road. If the banking angle is $45^o$, the speed of the car is ......... $ms^{-1}$