Circular Motion Question

1. The problem statement, all variables and given/known data
What must be the period of rotation of the Earth on its axis so that a person at the equator will have a reading on the scale that is approximately one fifth as much as he would at the North Pole?

(Given on the formula sheet)
Radius of Earth = 6.37 x 10^6 m

2. Relevant equations
Fc = m*ac
ac = (4*(pi^2)*r)/(T^2)
Fg = m*g

3. The attempt at a solution
I had tried making Force of gravity (Fg) equal to Centripetal Force (Fc), then solving for T. Though this gives me an answer that is close to the one that my teacher gave me, the process doesn’t feel right. I then tried repeating the process, but first multiplying Fg by 1/5 (as stated in the question), however, this also doesn’t give me the right answer.

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