X and Y are two loops made from same wire. The radii of X and Y are `r_(1)` and `r_(2)` and their M.I are `I_(1)` and `I_(2)` . If `I_(2)//I_(1)=4` the value of `r_(2)/r_(1)` is `(K)^(1//3)`. Find the value of K.

Explanation

To solve the problem, we need to find the value of \( K \) given that the moment of inertia ratio \( \frac{I_2}{I_1} = 4 \) and the relationship \( \frac{r_2}{r_1} = K^{1/3} \).

### Step-by-Step Solution

1. **Understand the Moment of Inertia**: The moment of inertia \( I \) of a loop (ring) is given by the formula:
\[ I = m r^2 \]
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