in air an object weighs 15N. when immersed in water it weighs 12 N. when immersed in another liquid it weighs 13 N.determine the density of the object and that of the other liquid
I want an answer
density*volume is mass
so
density*V=15
12=15-densitywater*V
13=15-desnityLiquid*V
You know densitywater. You are left with two equations, two unknowns. I assume you can handle that
V=15/densityobject
use 12=15-densitywater*15/densityobject now to solve for density
then the final equation to find densityliquid
To determine the density of the object and the other liquid, we can apply Archimedes' principle. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
1. Density of the Object:
Using Archimedes' principle, we can find the volume of the object. The weight of the object in air is given as 15 N. Therefore, the volume of the object is equal to the weight of the fluid it displaces in air, divided by the density of air.
However, the density of air is very low compared to liquids, so we can often neglect it. In this case, we can approximate the volume of the object as the weight of the object in air divided by the density of water.
Using this approximation, the volume of the object is:
Volume = Weight in air / Density of water
Volume = 15 N / Density of water
Now, to calculate the density of the object, we need to divide its mass by its volume.
Density = Mass / Volume = Mass / (15 N / Density of water)
2. Density of the Other Liquid:
Similarly, we can apply Archimedes' principle to find the density of the other liquid. The weight of the object when immersed in this liquid is given as 13 N. Again, we can approximate the volume of the object as the weight of the object in this liquid divided by the density of this liquid.
The volume of the object in this liquid is:
Volume = Weight in the other liquid / Density of the other liquid
Volume = 13 N / Density of the other liquid
Now, to calculate the density of the other liquid, we divide its mass by its volume.
Density of the other liquid = Mass / Volume = Mass / (13 N / Density of the other liquid)
By setting up two equations for the density of the object and the other liquid, we can solve them simultaneously to find their values.