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

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To calculate the radius of the submerged iron ball, the discussion emphasizes treating the floating cylinder and the submerged ball as separate objects. The cylinder's dimensions and density are provided, with a focus on the buoyant force acting on it. The equation p(liq)gV(obj) = Mg is suggested as a starting point for the calculations, indicating a relationship between the liquid density, gravitational force, and the volume of the object. The approach of analyzing the floating object first is deemed appropriate. Ultimately, understanding the forces acting on both the cylinder and the ball is crucial for solving the problem 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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