Pg:- 8 and 9 chapter-1

Density is a fundamental property of matter that describes the mass of a substance per unit volume.

The basic formula for calculating density (ρ) is:

ρ= m/V

• ρ (rho) represents density,

• m is the mass of the substance,

• V is the volume of the substance.

• The SI unit of density is kilograms per cubic meter (kg/m³).

• Commonly used units include grams per cubic centimeter (g/cm³) and grams per milliliter (g/mL), particularly in laboratory settings.

Steps to Calculate Density

1. Measure the Mass:

   • Use a balance to measure the mass of the substance. Ensure the balance is calibrated and precise.

   • Record the mass in appropriate units (grams or kilograms).

2. Measure the Volume:

   • Regular Shapes: For objects with regular geometric shapes (e.g., cubes, spheres), calculate the volume using geometric formulas.

     • Cube: V = a^3 (where a is the side length)

     • Sphere: V=4/3πr^2  (where r is the radius)

     • Cylinder: V=πr^2h (where r is the radius and h is the height)

   • Irregular Shapes: For irregularly shaped objects, use the water displacement method or volume calculation using a graduated cylinder.

     • Fill a graduated cylinder with a known volume of water.

     • Submerge the object in the water and record the new volume.

     • The volume of the object is the difference between the initial and final volumes of water.

3. Calculate Density:

   • Use the measured mass and volume in the density formula to calculate the density.

   • Ensure the units of mass and volume are compatible (e.g., grams and cubic centimeters or kilograms and cubic meters).

Example

• Given: A cube with a side length of 2 cm and a mass of 16 g.

• Volume: V = a^3 = 2^3 = 8 cm^3

• Mass: m = 16g

• Density: ρ = m/v = 16g/8cm^3 = 2 g/cm^3