Pendulum Problem and steiner' law

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The discussion focuses on calculating the period of a uniform circular disk acting as a physical pendulum and finding an alternative pivot point that yields the same period. The period is calculated using the formula T = 2π√(I/mgh), with the correct answer for part A being 0.849 seconds. For part B, participants suggest using Steiner's law to express the moment of inertia (I) through a parallel axis. The goal is to equate the period of the disk to that of a simple pendulum to determine the radial distance r. The conversation emphasizes the application of physics principles to solve the problem effectively.
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Homework Statement


A uniform circular disk whose radius R is 14.3 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period? (b) At what radial distance r < R is there a pivot point that gives the same period? (give answer in cm)

Homework Equations


T= 2pi radical ( I / mgh )

The Attempt at a Solution


Okay, I already found part A using T= 2pi radical ( I / mgh )
Any help would be greatly appreciated =]

Part A: 0.849 s <-- It's correct.
I'm just stuck on Part B.
 
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Use steiner' law to express the I through a parallel axis..
 
You can find the radial distance by equating period of the disk to that of a simple pendulum.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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