Find the ratio of radii of gyration of a hollow cylinder and a solid cylinder about an axis passing through their centres and parallel to length.

Explanation

To find the ratio of the radii of gyration of a hollow cylinder and a solid cylinder about an axis passing through their centers and parallel to their lengths, we can follow these steps:

### Step 1: Understand the Moment of Inertia
The moment of inertia (I) of an object is related to its mass (m) and the radius of gyration (k) by the formula:
\[ I = m k^2 \]

### Step 2: Moment of Inertia for Hollow Cylinder
For a hollow cylinder, the moment of inertia about an axis through its center and parallel to its length is given by:
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