Answer:
Rotational inertia of the object is, 
Explanation:
Given that,
Mass of the object, m = 20 kg
Torsion constant of the wire, K = 0.85 N-m
Number of cycles, n = 69
Time, t = 66 s
To find,
The rotational inertia of the object.
Solution,
There exists a relationship between the moment of inertia, time period and the torsion constant of the spring is given by :

Here I is the moment of inertia
T is the time period, and it is equal to the number of cycles per unit time



So, the rotational inertia of the object is
.
The hang time of the ball is 4.08 s
Explanation:
The ball is in free fall motion: this means that it is acted upon gravity only, so its acceleration is the acceleration of gravity,

downward (the negative sign refers to the downward direction).
Since this is a uniformly accelerated motion, we can solve the problem by using the following suvat equation:

where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
First we calculate the time it takes for the ball to reach the maximum height, where the velocity is zero:
v = 0
Substituting:
u = +20 m/s

we find t

The motion of the ball is symmetrical, so the total time of flight is just twice the time needed to reach the maximum height, therefore:

Learn more about free fall:
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Due to Ohm's law, I is proportional to V and 1/R:
I ∝ V
I ∝ 1/R
R is proportional to the wire length L:
R ∝ L
Therefore I is also proportional to 1/L:
I ∝ 1/L
Calculate the scale factor due to increased voltage:
k₁ = 24/12 = 2
Calculate the scale factor due to decreased wire length:
k₂ = 1/(0.5/1) = 2
Multiply the original current by the scale factors to get the new current:
I = I₀k₁k₂
I₀ = 100mA, k₁ = 2, k₂ = 2
I = 100(2)(2)
I = 400mA