Identical charged particles are accelerated through the same potential difference, and then made to enter in a region of uniform magnetie field. If `R_(1) " and " R_(2)` , are the radii of a circular paths followed by particles then what will be the ratio of their masses.

Explanation

To solve the problem, we need to find the ratio of the masses of two identical charged particles that are accelerated through the same potential difference and then enter a uniform magnetic field, where they follow circular paths with radii \( R_1 \) and \( R_2 \).

### Step-by-step Solution:

1. **Understanding the Motion in Magnetic Field:**
When a charged particle enters a magnetic field, it experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path. The centripetal force \( F_c \) is given by:
\[
F_c = \frac{mv^2}{R}
...