Two particles `X` and `Y` having equal charges, after being acceleration through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii `R_1` and `R_2`, respectively. The ratio of the mass of `X` to that of `Y` is

Options

A. `(R_1//R_2)^(1//2)`
B. `R_2//R_1`
C. `(R_1//R_2)^2`
D. `R_1//R_2`

Explanation

To solve the problem, we need to find the ratio of the masses of two particles \(X\) and \(Y\) based on their circular paths in a magnetic field after being accelerated through the same potential difference. Here’s a step-by-step solution:

### Step 1: Understand the relationship between kinetic energy and potential energy
When the particles are accelerated through the same potential difference \(V\), the gain in kinetic energy (\(KE\)) is equal to the loss in potential energy (\(PE\)):
\[ KE = PE \]
The kinetic energy gained by each particle can be expressed as:
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