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
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Answer:
819.78 m
Explanation:
<u>Given:</u>
- OA = range of initial position of the airplane from the point of observation = 375 m
- OB = range of the final position of the airplane from the point of observation = 797 m
= angle of the initial position vector from the observation point = 
= angle of the final position vector from the observation point = 
= displacement vector from initial position to the final position
A diagram has been attached with the solution in order to clearly show the position of the plane.

Displacement vector of the airplane will be the shortest line joining the initial position of the airplane to the final position of the airplane which is given by:

The magnitude of the displacement vector = 
Hence, the magnitude of the displacement of the plane is 819.67 m during the period of observation.
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D. since the star would be larger than the sun, having more mass, its gravitational pull would be stronger thus pulling the planets into it. hope that helped!