Which of the following particles will experience maximum acceleration when projected with the same speed in a transverse magnetic field?

An $\alpha$-particle (mass $4 \text{ amu}$) and a singly charged sulfur ion (mass $32 \text{ amu}$) 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 $r_s$,respectively. The ratio $(r_s / r_\alpha)$ is:

$A$ positive charge particle having charge $q$ and mass $m$ has velocity $\vec v = v\left( {\frac{{\hat i + \hat k}}{{\sqrt 2 }}} \right)$ in the magnetic field $\vec B = B\hat j$ and electric field $\vec E = E\hat j$ at the origin. Its speed as a function of $y$ is:

An electron falling freely under the influence of gravity enters a uniform magnetic field directed towards the south. The electron is initially deflected towards:

$A$ beam of protons with speed $4 \times 10^{5} \ m/s$ enters a uniform magnetic field of $0.3 \ T$ at an angle of $60^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to....$cm$
(Mass of the proton $= 1.67 \times 10^{-27} \ kg$, charge of the proton $= 1.6 \times 10^{-19} \ C$)

Work done by a magnetic field of $1\,T$ on a particle of charge $1\,C$ moving with a speed of $5\,m/s$ in one second is........$J$.