Check your answer and give me the final answer : Why is the following situation

Question

Check your answer and give me the final answer :

Why is the following situation impossible? A space station shaped like a giant wheel has a radius of r = 100 m and a moment of inertia of 5.00 times 10^8 kg middot m^2. A crew of 150 people of average mass 65.0 kg is living on the rim, and the station's rotation causes the crew to experience an apparent free-fall acceleration of g (see figure below). A research technician is assigned to perform an experiment in which a ball is dropped at the rim of the station every 15 minutes and the time interval for the ball to drop a given distance is measured as a test to make sure the apparent value of g is correctly maintained. One evening, 100 average people move to the center of the station for a union meeting. The research technician, who has already been performing his experiment for an hour before the meeting, is disappointed that he cannot attend the meeting, and his mood sours even further by his boring experiment in which every time interval for the dropped ball is identical for the entire evening.

Explanation / Answer

Using Conservation of energy,

K.E. of the space wheel intially = K.E. of space wheel when 100 people are in centre

I² =I''²r

Here I' is smaller than I. ( Since mass moves to center, for point masses, moment of inertia = m^2 r)

' is bound to be greater than .

The gravitational acceleration

g = ²r   

g' = '²r

g' is greater.

Hense. The time taken in second case should be smaller instead of being same in both the case.

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