in air, an object weights 15N. when immersed in water, it weights 12N. when immersed in another liquid, its weights 13N. determine the density of the object, the relative density of the object and the density of the other liquid?
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To determine the density of the object, the relative density of the object, and the density of the other liquid, we need to understand the principles of buoyancy and Archimedes' principle.
1. Density of the object:
The density of an object is defined as its mass per unit volume. We can use Archimedes' principle to find the density of the object.
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
In air, the weight of the object is 15N, which is also its mass. Therefore, the volume of the object is 15N divided by the density of air (approximately 1.2 kg/m³). Thus, the volume of the object is 15N / 1.2 kg/m³ = 12.5 m³.
Since we now know the mass and volume of the object, we can calculate its density. The density (ρ) is equal to mass (m) divided by volume (V). So, ρ = 15N / 12.5 m³ ≈ 1.2 kg/m³.
Therefore, the density of the object is approximately 1.2 kg/m³.
2. Relative density of the object:
The relative density of an object is the ratio of its density compared to the density of a reference substance. In this case, we will use water as the reference substance.
The density of water is approximately 1000 kg/m³. Therefore, the relative density of the object is ρ/ρ_water = 1.2 kg/m³ / 1000 kg/m³ = 0.0012.
Therefore, the relative density of the object is 0.0012.
3. Density of the other liquid:
To find the density of the other liquid, we can use the same approach as mentioned earlier.
When immersed in the other liquid, the weight of the object is 13N. We already know the mass of the object is 15N. So, the volume of the object can be calculated as 15N / 13N = 1.15 times the volume in air (12.5 m³).
Since the volume is 1.15 times the original volume, the density of the other liquid can be calculated using the formula: ρ_other_liquid = 15N / (1.15 * 12.5 m³).
Therefore, the density of the other liquid is approximately ρ_other_liquid = 1.04 kg/m³.
In summary:
- Density of the object is approximately 1.2 kg/m³.
- Relative density of the object is 0.0012.
- Density of the other liquid is approximately 1.04 kg/m³.
the object displaces 1/5 of its weight in water, so it is 5 times the density of water
the weight change in the other liquid is 2/3 of the change in water, so the other liquid is 2/3 the density of water