How Do You Calculate the Radius of a Submerged Iron Ball?

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SUMMARY

The discussion focuses on calculating the radius of a submerged iron ball attached to a floating cylinder. The cylinder, with a height of 6.00 cm and a density of 0.30 g/cm³, has 2.00 cm of its height above water. The correct approach involves applying the equation p(liq)gV(obj) = Mg, treating the forces acting on both the submerged ball and the floating cylinder separately to find the radius of the ball accurately.

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An iron ball is suspended by a thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 6.00 cm, a face area of 12.0 cm^2 on the top and bottom, and a density of 0.30 g/cm^3. 2.00 cm of its height is above the surface. What is the radius of the iron ball?

The ball is completely submerged but the cylinder is floating so which a should I solve it first, submerged or floating. I'm approaching it as a floating object right now.

Using the equation p(liq)gV(obj)= Mg

Is this in the right direction?
 
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I would treat each object separately, considering all the forces on them.
 

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