If the radii of circular path of two particles are in the ratio of `1 :2`, then in order to have same centripetal acceleration, their speeds should be in the ratio of :

Options

A. `1:4`
B. `4:1`
C. `1: sqrt(2)`
D. `sqrt(2):1`

Explanation

To solve the problem, we need to find the ratio of speeds of two particles moving in circular paths with radii in the ratio of 1:2, while maintaining the same centripetal acceleration.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the radius of the first particle be \( r_1 \) and the radius of the second particle be \( r_2 \). According to the problem, the ratio of the radii is given as:
\[
\frac{r_1}{r_2} = \frac{1}{2}
...