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
Answer:
N= 238 turns
Explanation:
The induced Emf that goes through a solenoid can be calculated using the below formula;
Where ξ=induced Emf
L= self inductance
I= current
ξ= L|dⁱ/dt|
Making L which is the self inductance subject of formula we have
L=ξ/[|dⁱ|*|dt|]
The current here is changing at the rate of
.0260 A/s
L=NΦB/i
N=ξ/Φ|di|*|dt|
Magnitude of the induced Emf given= 12.6mV then if we convert to volt we have 12.6×10⁻³ V
The current I = 1.40A
Magnitude flux through the flux=/0.00285 Wb
Then if we substitute all this Value to equation above we have
N=(12.6×10⁻³ V×1.40A)/(0.00285 Wb×0.0260 A/s)
N=238turn
Therefore, there are 238turns in the solenoid
The very first option is correct, as any other answer is either incorrect in terms of optics or does not stop you from seeing the apple.
Answer:
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