Final answer:
To find the relative density of a cork, we use the given weights of the cork in air, the sinker in water, and the combination of both in water, applying the concept of buoyancy and Archimedes' principle.
Step-by-step explanation:
Let's tackle this problem step by step.
First, let's define some terms and symbols to make the explanation clearer:
- "gf" stands for gram-force, a unit of force equal to the gravitational force acting on a mass of one gram.
- "r.d." stands for relative density, also known as specific gravity, which is a ratio that compares the density of a substance to the density of water. Since the density of water is approximately 1 g/cm³ at 4°C, for solids and liquids, the r.d. is numerically equivalent to the density in the units of g/cm³.
Given:
- Weight of cork in air = 4 gf
- Weight of cork + sinker in water = 30 gf
- Weight of sinker alone in water = 34 gf
We know that when an object is submerged in a fluid (in this case, water), it experiences an upward buoyant force equal to the weight of the fluid it displaces. The apparent weight of the object in water is its actual weight minus the buoyant force.
Now, let's find the weight of the cork in water. When the cork is tied to the sinker and submerged in water, the total weight is the weight of both the cork and the sinker minus the water's buoyant force on both.
Apparent weight of cork in water = Actual weight of cork in air - Buoyant force
The buoyant force on the cork is the difference between its weight in air and its apparent weight in water.
The apparent weight of the cork in water can be found by considering the difference in weight of the sinker alone in water and the combination of sinker + cork in water:
Apparent weight of cork in water = Weight of sinker alone in water - Weight of sinker + cork in water
Apparent weight of cork in water = 34 gf - 30 gf
Apparent weight of cork in water = 4 gf
Now we can see that the apparent weight of the cork in water is the same as its actual weight in air. This means that the weight of the cork is completely balanced by the buoyant force on it when submerged, implying that the cork is of the same density as water (since it's neither sinking nor floating).
Therefore, the relative density (r.d.) of the cork is 1, because its density is the same as the density of water. This means that the cork has the same specific gravity as water, which is 1.