Question

2. In his experiment, to test whether the crown of the King of Sycaruse was made of pure gold or not, Archimedes immersed the crown into a container filled with water. He noted that the crown displaced 150 mL of water. If the mass of the crown is 2675 g, is it made of pure gold? Prove your answer with computations.

Answer 1

As 2.675 kg is greater than 0.15 kg, the crown is made of a substance that has a higher density than water and therefore is not made of pure gold. In his experiment, Archimedes used his principle of buoyancy to determine whether the crown was made of pure gold or not. He compared the weight of the crown to the weight of the water it displaced. If the crown was made of pure gold, it would have the same density as gold, which is higher than that of water. By calculating the weights and densities, Archimedes concluded that the crown is not made of pure gold.

Step-by-step explanation:

Archimedes used his principle of buoyancy to determine whether the crown was made of pure gold or not.

According to Archimedes' principle, the buoyant force acting on a submerged object equals the weight of the fluid it displaces.

He measured the amount of water displaced by the crown and compared it to the weight of the crown.

If the crown was made of pure gold, it would have the same density as gold, which is higher than that of water.

Therefore, the weight of the water displaced by the crown should be less than the weight of the crown. L

et's calculate:

Given:
Mass of the crown (m) = 2675 g
Volume of water displaced (V) = 150 mL = 150 cm³

1. Since the density (ρ) of gold is higher than that of water, the weight of the crown (Wc) should be greater than the weight of the water displaced (Ww):

Wc > Ww

2. The weight of the crown can be calculated using the formula:

Wc = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s²).

3. The weight of the water displaced can be calculated using the formula:

Ww = ρw * V * g
where ρw is the density of water (approximately 1000 kg/m³).

4. Comparing the weights:

m * g > ρw * V * g

5. Canceling out the g's:

m > ρw * V

6. Converting the mass and volume to appropriate units:

m = 2675 g = 2.675 kg
V = 150 cm³ = 0.15 L = 0.15 dm³

7. Substituting the values:

2.675 kg > 1000 kg/m³ * 0.15 dm³

8. Converting the volume to m³:

2.675 kg > 1000 kg/m³ * 0.15 * 10⁻³ m³

9. Solving the equation:

2.675 kg > 0.15 kg