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

[xgoodtimesx]

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

 

[tiny-tim]

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