A flat bottomed loaded test –tube sinks to a depth of 10 cm in a liquid and 12 cm in water. Calculate the relative density of the liquid.
Question
A flat bottomed loaded test –tube sinks to a depth of 10 cm in a liquid and 12 cm in water. Calculate the relative density of the liquid.
Solution
The relative density of a substance is the ratio of the density of the substance to the density of a reference substance. In this case, we are comparing the density of the liquid to the density of water.
The depth to which an object sinks in a fluid is inversely proportional to the density of the fluid. This means that the ratio of the depths to which the test tube sinks in the liquid and in water is equal to the ratio of the densities of water and the liquid.
So, we can set up the following equation:
Density of liquid / Density of water = Depth in water / Depth in liquid
We know that the density of water is 1 g/cm^3, the depth in water is 12 cm, and the depth in the liquid is 10 cm. Substituting these values into the equation gives us:
Density of liquid / 1 g/cm^3 = 12 cm / 10 cm
Solving for the density of the liquid gives us:
Density of liquid = 1 g/cm^3 * (12 cm / 10 cm) = 1.2 g/cm^3
Therefore, the relative density of the liquid is 1.2.
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