An $\alpha $ particle and a proton travel with same velocity in a magnetic field perpendicular to the direction of their velocities, find the ratio of the radii of their circular path

A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. the radius of the circular portion of the path is :-

An electron having kinetic energy $T$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic induction $\vec B$ . If kinetic energy is doubled and magnetic induction tripled, the radius will become 

A current carrying long solenoid is placed on the ground with its axis vertical. A proton is falling along the axis of the solenoid with a velocity $v$. When the proton enters into the solenoid, it will

An electron moving with a velocity ${\vec V_1} = 2\,\hat i\,\, m/s$ at a point in a magnetic field experiences a force ${\vec F_1} =  - 2\hat j\,N$ .  If the electron is moving with a velocity ${\vec V_2} = 2\,\hat j \,\,m/s$ at the same point, it experiences a force ${\vec F_2} =  + 2\,\hat i\,N$ .  The force the electron would experience if it were moving with a velocity ${\vec V_3} = 2\hat k$  $m/s$ at the same point is

An electron accelerated through a potential difference $V$ enters a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$, the electron in the same magnetic field will experience a force