An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_e, R_p, R_d \,$ and $\, R_\alpha$. It follows that

A particle with charge to mass ratio, $\frac{q}{m} = \alpha $ is shot with a speed $v$ towards a wall at a distance $d$ perpendicular to the wall. The minimum value of $\vec B$ that exist in this region perpendicular to the projection of velocity for the particle not to hit the wall is

A singly ionized magnesium atom $(A=24)$ ion is accelerated to kinetic energy $5\,keV$ and is projected perpendicularly into a magnetic field $B$ of the magnitude $0.5\,T$. The radius of path formed will be___________ $cm$

A particle having the same charge as of electron moves in a circular path of radius $0.5
\,cm$ under the influence of a magnetic field of $0.5\,T.$ If an electric field of $100\,V/m$ makes it to move in a straight path, then the mass of the particle is (given charge of electron $= 1.6 \times 10^{-19}\, C$ )

A particle having some charge is projected in $x-y$ plane with a speed of $5\ m/s$ in a region having uniform magnetic field along $z-$ axis. Which of the following cannot be the possible value of velocity at any time ?

Bob of a simple pendulum of length $l$ is made of iron . The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is $T$ then