Problem: Materials #1

An object has a weight of 4 N in air, 3 N in water and 2.8 N in a salt solution. If the density of water is 1000 kg m^-3, the density of the salt solution is
A. 830 kg m^-3
B. 1070 kg m^-3
C. 1200 kg m^-3
D. 1430 kg m^-3

Solution

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The answer is C.

This is a problem that requires the application of Archimedes’ principle.

The object has a weight of 4 N in air. Because the upthrust on the object when it is in air is negligible, we can say that the weight of the object is 4 N.

When the object is (completely immersed) in water, its weight is 3 N, so it experiences an apparent loss of weight of 1 N due to the upthrust acting on the object.

Upthrust = Apparent loss of weight
and
Upthrust = Vρ_waterg

Where
V – volume of the object
ρ_water – density of water
g – the acceleration due to gravity

Now the object is immersed in a salt solution with density ρ_salt and its weight becomes 2.8 N. It experiences an apparent loss of weight of 1.2 N, therefore
Upthrust = Vρ_saltg = 1.2 N - (2)

Because the volume of object remains the same, we substitute equation 1 into equation 2.

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Question source: Malaysia National Physics Competition Panel