Here is the full question:
The rotational inertia I of any given body of mass M about any given axis is equal to the rotational inertia of an equivalent hoop about that axis, if the hoop has the same mass M and a radius k given by:

The radius k of the equivalent hoop is called the radius of gyration of the given body. Using this formula, find the radius of gyration of (a) a cylinder of radius 1.20 m, (b) a thin spherical shell of radius 1.20 m, and (c) a solid sphere of radius 1.20 m, all rotating about their central axes.
Answer:
a) 0.85 m
b) 0.98 m
c) 0.76 m
Explanation:
Given that: the radius of gyration
So, moment of rotational inertia (I) of a cylinder about it axis = 





k = 0.8455 m
k ≅ 0.85 m
For the spherical shell of radius
(I) = 




k = 0.9797 m
k ≅ 0.98 m
For the solid sphere of radius
(I) = 




k = 0.7560
k ≅ 0.76 m
Is it a magnifying glass?
It is not an example of kinetic to potential because the dog is already in motion rather then having the potential to do something. Hope this helps!
The refractive index is the ratio of the speed in a vacuum to the speed of light in the given medium. If the refractive index is too low, there will not be a large bending, or deviation, of the light beam from its original path.
The small deviation will make it difficult to carry out the experiment, and is more likely to cause errors. Therefore, larger refractive indexes should be used, in order to ensure that the bending of the light beams is easily traceable.