How Is the Density of the Rock Determined in a Buoyancy Problem?

AI Thread Summary
The discussion focuses on determining the density of a rock using buoyancy principles involving a cork and two different liquids. The cork has a known density of 0.24 g/cm³ and exhibits different submersion fractions in two liquids with densities of 0.80 g/cm³ and 0.89 g/cm³. To solve for the rock's density, an equation must be derived based on the buoyant forces acting on the cork in both liquids. Participants are encouraged to share their attempts and specific challenges to facilitate assistance. The conversation emphasizes collaborative problem-solving in physics.
xgoodtimesx
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One end of a light thin string is attached to a cork with density ρC = 0.24 g/cm3. The other end is attached to a rock. When the arrangement is placed in liquid 1 with density ρ1 = 0.80 g/cm3, a fraction f1 = 0.75 of the cork becomes submerged. When the arrangement is placed in liquid 2 with density ρ2 = 0.89 g/cm3, a fraction f2 = 0.67 of the cork becomes submerged. What is the density of the rock?


Please derive a equation to solve this problem
 
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