Two uniform circular loops A and B of radii r and nr are made of the same uniform wire. If moment of inertia of A about its axis is twice that of B, then find the value of n [diameter of wire is much smaller compared to radii of the loops].

Explanation

To solve the problem, we need to find the value of \( n \) given that the moment of inertia of loop A is twice that of loop B. Let's go through the solution step by step.

### Step 1: Define the Moments of Inertia
The moment of inertia \( I \) of a circular loop about its axis is given by the formula:
\[ I = m r^2 \]
where \( m \) is the mass of the loop and \( r \) is its radius.
...