A rock is suspended by a light string. When the rock is in air, the tension in the string is 39.2 N. When the rock is totally immersed in water, the tension is 28.4 N. When the rock is totally immersed in an unknown liquid, the tension is 21.5 N. What is the density of the unknown liquid?

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Answer:1638.89 kg/m³Explanation:From the question,

R.D = Upthrust of the rock in liquid/upthrust of the rock in water = Density of liquid/Density of water.

U’/U = D’/D………………………. Equation 1

Where U’ = Upthrust in liquid = Weight of rock in air- weight of rock in liquid,

U = Upthrust in water = weight of rock in air – weight of rock in water, D’ = Density of liquid, D = Density of water.

make D’ the subject of the equation

D’ = (U’/U)D………………. Equation 2

Given: U’ = 39.2-21.5 = 17.7 N, U = 39.2-28.4 = 10.8 N

Constant: D = 1000 kg/m³

Substitute these values into equation 2

D’ = (17.7/10.8)1000

D’ = 1638.89 kg/m³