A rock is suspended by a light string. When the rock is in air, the tension in the string is 43.8 . When the rock is totally immersed in water, the tension is 26.2 . When the rock is totally immersed in an unknown liquid, the tension is 18.8 .
Your numbers require units. That is one of the first lessons you ahould have learned about physics.
To find the density of the unknown liquid, we need to use Archimedes' principle, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The buoyant force is given by the formula:
Buoyant force = weight of fluid displaced = density of fluid × volume of fluid displaced × acceleration due to gravity
Let's assume the density of the rock to be ρr, the density of water to be ρw, and the density of the unknown liquid to be ρl. The weight of the rock can be given by:
Weight of the rock = mass of the rock × acceleration due to gravity = ρr × volume of the rock × acceleration due to gravity
When the rock is in the air, the tension in the string is equal to the weight of the rock:
Tension in air = ρr × volume of the rock × acceleration due to gravity
When the rock is in water, it experiences a buoyant force equal to the weight of the water it displaces:
Buoyant force in water = ρw × volume of the rock × acceleration due to gravity
Therefore, the tension in water is equal to the weight of the rock minus the buoyant force:
Tension in water = Tension in air - Buoyant force in water
= ρr × volume of the rock × acceleration due to gravity - ρw × volume of the rock × acceleration due to gravity
We can simplify this equation by factoring out the volume of the rock:
Tension in water = (ρr - ρw) × volume of the rock × acceleration due to gravity
Similarly, when the rock is in the unknown liquid, the tension can be given by:
Tension in unknown liquid = (ρr - ρl) × volume of the rock × acceleration due to gravity
We are given the values of tensions in air, water, and the unknown liquid, so we can write the following equations:
Tension in air = (ρr - ρw) × volume of the rock × acceleration due to gravity
Tension in water = (ρr - ρw) × volume of the rock × acceleration due to gravity
Tension in unknown liquid = (ρr - ρl) × volume of the rock × acceleration due to gravity
We can rearrange the equation for the unknown liquid's density:
(ρr - ρl) = Tension in unknown liquid / (volume of the rock × acceleration due to gravity)
Now we have all the values needed to find the density of the unknown liquid.