Final answer:
To calculate the relative density of the metal, use Hooke's law and the extension of the spring in air and water. The ratio of the forces applied to the spring in air and water will give you the relative density of the metal.
Step-by-step explanation:
To calculate the relative density of the metal, we can use Hooke's law, which states that the extension of a spring is directly proportional to the force applied to it. In this case, the spring extends by 10.5 cm in air and 6.8 cm when the metal is submerged in water. The difference in extension is caused by the buoyant force acting on the metal when it is submerged.
We can calculate the force applied to the spring in both cases using the formula F = kx, where F is the force, k is the spring constant, and x is the extension. The ratio of the forces in air and water will give us the relative density of the metal.
Let's assume the spring constant is the same for both cases:
Fair = k * 10.5 cm
Fwater = k * 6.8 cm
The relative density can be calculated as:
Relative Density = Fair / Fwater
By substituting the values of Fair and Fwater into the formula, we can find the relative density of the metal.