Final answer:
The volume of water with the same mass as 100 mm3 of gold is 1.93 cm³. The density of gold is 19.3 g/cm³, and using the formula for specific weight which is density times gravity, the specific weight of gold is 189.273 N/m³.
Step-by-step explanation:
The density of gold is given as 19.3 g/cm³. First, we need to convert the volume from mm³ to cm³ since there are 1,000 mm³ in 1 cm³. So, 100 mm³ of gold is equal to 0.1 cm³ of gold. Using the density of gold, we can calculate the mass of this volume of gold which would be mass = density × volume. Thus, mass = 19.3 g/cm³ × 0.1 cm³ = 1.93 g.
The density of water is 1 g/cm³ by definition. Therefore, to find the volume of water that has the same mass, we divide the mass of gold by the density of water. Hence, the volume of water = mass / density of water = 1.93 g / 1 g/cm³ = 1.93 cm³.
The specific weight of gold can be found by multiplying its density by the acceleration due to gravity. Since the acceleration due to gravity is approximately 9.81 m/s², the specific weight of gold = density of gold × gravity = 19.3 g/cm³ × 9.81 m/s². To convert g/cm³ to kg/m³ and have consistent units, we multiply by 1,000, which gives us a specific weight of gold as 189.273 N/m³.