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A body weighs 0.45 N in air. Totally immersed in water, it weighs only 0.22 N, while when immersed in another liquid, it is 0.26 N. Determine the density of the other liquid.

A. 0.5 g/cm³
B. 0.6 g/cm³
C. 0.7 g/cm³
D. 0.8 g/cm³

User Odinn
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1 Answer

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Final answer:

Using Archimedes' Principle and the given buoyant forces in water and an unknown liquid, the density of the unknown liquid is calculated to be approximately 0.8 g/cm³, which corresponds to the answer choice D.

Step-by-step explanation:

The problem you've presented involves finding the density of an unknown liquid using the principle of buoyancy, as described by Archimedes' Principle. Since the body weighs 0.45 N in air and only 0.22 N when totally immersed in water, the buoyant force of water on the body is 0.45 N - 0.22 N = 0.23 N. Similarly, when the body is immersed in the unknown liquid, the weight is 0.26 N, so the buoyant force of this liquid is 0.45 N - 0.26 N = 0.19 N.

To find the density of the liquid, we realize that the buoyant forces are proportional to the densities of the fluids. Since we know the density of water is 1 g/cm³ (or equivalently, 1000 kg/m³), and the buoyant force due to water is 0.23 N, we can set up a proportion:

Buoyant force in water / Density of water = Buoyant force in unknown liquid / Density of unknown liquid

0.23 N / 1 g/cm³ = 0.19 N / Density of unknown liquid

Therefore, Density of unknown liquid = (0.19 N / 0.23 N) * 1 g/cm³ = 0.826 g/cm³ ≈ 0.8 g/cm³. The closest answer option that matches this calculation is D. 0.8 g/cm³.

User Robert Kock
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