An alpha particle and proton enter a region of magnetic field which is perpendicular to their direction of motion. Find ratio of radius of circle described by them if they
(i) have same velocity
(ii) have same momentum
(iii) have same energy
(iv) are accelerated by same potential difference

Explanation

To solve the problem of finding the ratio of the radius of the circular path described by an alpha particle and a proton in a magnetic field under different conditions, we will analyze each case step by step.

### Given:
- Mass of proton, \( m \)
- Charge of proton, \( Q \)
- Mass of alpha particle, \( 4m \)
- Charge of alpha particle, \( 2Q \)
- Magnetic field, \( B \)
...