From a uniform wire, two circular loops are made. One loop P of radius r and the other Q of radius nr. If the moment of inertia of Q about an axis passing through its center and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr):

Determine the two loops' moment of inertia in terms of their masses and radii. Try to link P and Q's masses in terms of 'n' because they will have different masses. Then, using the criterion stated in the question, compare them to determine n.
Equation used:

$MOI=M{R}^2$, about a perpendicular axis running through the center of a ring.

Step 1: Create a diagram with labels.
Step 2: Identify n's value.
Given,
Radius of $\mathrm{P},\mathrm{R}=\mathrm{r}$
Radius of $Q,R=nr$
$\frac{I_Q}{I_P}=8$
As we know,
Mass $\propto$ length
$m_p=m,m_Q=nm$
$\frac{I_Q}{I_P}=\frac{\left(nm\right)(nr{)}^2}{m{r}^2}=8$
$n^3=8\Rightarrow n=2$

Hence, the correct answer is option D.