Density

Density (ρ) = mass (m) / volume (V)

m = 250g = 0.25 kg
V = 100 cm³ = 100 x 10⁻⁶ m³ = 1 x 10⁻⁴ m³

ρ = 0.25 kg / (1 x 10⁻⁴ m³)
ρ = 2500 kg/m³

Density is calculated by dividing the mass by the volume. We converted the given mass and volume to SI units (kg and m³ respectively) before calculation.

Density is mass per unit volume. Polystyrene has a low density, meaning that a given volume of polystyrene has a small mass, smaller than the mass of the same volume of water. Because it is less dense than water, it floats. The stone has a high density - a given volume has a large mass, larger than the mass of the same volume of water. Because it is more dense than water, it sinks.

1. Calculate the volume of the spheres:
Volume of spheres = Final volume - Initial volume = 65 cm³ - 50 cm³ = 15 cm³

2. Calculate the volume of one sphere:
Volume of one sphere = Total volume / Number of spheres = 15 cm³ / 10 = 1.5 cm³

3. Calculate the mass of one sphere:
Mass of one sphere = Total mass / Number of spheres = 150 g / 10 = 15 g

4. Calculate the density:
Density = Mass / Volume = 15 g / 1.5 cm³ = 10 g/cm³

*Density of the metal is 10 g/cm³*

1. Measure the mass: Use a balance to find the mass (m) of the stone in grams (g).

2. Measure the volume (using displacement):
* Partially fill a measuring cylinder with a known volume (V1) of water and record this volume.
* Carefully lower the stone into the measuring cylinder ensuring it is fully submerged. Make sure no water splashes out.
* Record the new volume (V2) of the water level.
* The volume of the stone (V) is the difference between the two readings: V = V2 - V1. The volume will be in cm³.

3. Calculate the density: Use the formula Density = Mass / Volume. Substitute the values of mass (m) and volume (V) to calculate the density of the stone in g/cm³.

*This method uses the principle of displacement to determine the volume of an irregularly shaped object.*

Density = Mass / Volume
Density of wood = 4.0 kg / 0.005 m³ = 800 kg/m³

Yes, the wood will float. The density of the wood (800 kg/m³) is less than the density of water (1000 kg/m³). Objects float if their density is less than the density of the fluid they are placed in.

The plastic ball floats because its density (800 kg/m³) is less than the density of water (1000 kg/m³). An object will float if it is less dense than the fluid it is in.

The glass marble sinks because its density (2500 kg/m³) is greater than the density of water (1000 kg/m³). An object will sink if it is more dense than the fluid it is in.

1. Identify which liquid floats:
Liquid A will float on Liquid B because Liquid A has a lower density (0.8 g/cm³) than Liquid B (1.2 g/cm³). Less dense objects float on more dense objects.

2. Calculate mass of Liquid A:
Density = Mass / Volume
Mass = Density x Volume
Mass of A = 0.8 g/cm³ x 50 cm³ = 40 g

3. Calculate mass of Liquid B:
Mass of B = Density x Volume
Mass of B = 1.2 g/cm³ x 50 cm³ = 60 g

4. Calculate the difference in mass:
Difference = Mass of B - Mass of A
Difference = 60 g - 40 g = 20 g

Answer: Liquid A will float on Liquid B. The mass difference is 20 g.

Liquid Y will float on top of Liquid X. This is because Liquid Y has a lower density (0.9 g/cm³) than Liquid X (1.1 g/cm³). Less dense liquids float on more dense liquids. The liquids will form two separate layers, with Liquid Y on top and Liquid X at the bottom.