Physical Quantities and Measurement Class 7 ICSE Physics Notes

Measurement of Volume

• Definition of Volume: All objects, whether solids, liquids, or gases, occupy space. The space occupied by an object is formally defined as its Volume.
• Comparative Example: A school hall is considered bigger than a classroom because the volume of air contained within the empty hall is greater than the volume of air in the empty classroom.
• S.I. Unit of Volume: The standard international unit for volume is the Cubic metre, denoted as $m^3$.
• Definition of 1 Cubic Metre: It is defined as the volume of a cube where each side measures exactly $1\,m$ in length.
• Volume Unit Conversions (Cubic Metre to Cubic Centimetre):
  • $1\,m^3 = 1\,m \times 1\,m \times 1\,m$
  • $1\,m^3 = 100\,cm \times 100\,cm \times 100\,cm$
  • $1\,m^3 = 1,000,000\,cm^3 = 10^6\,cm^3$
• Liquid Volume Units: The volume of a liquid is typically expressed in litres ($L$).
• Standard Conversions for Liquids:
  • $1\text{ litre} = 1000\,cm^3$
  • $1\,cm^3 = 10^{-3}\text{ litre} = 1\,mL$
• Capacity: This term is specifically used to express the volume of a vessel or a container.
• Cubic Decimetre ($dm^3$): This is another unit used for volume, sometimes referred to as $c.c.$.
  • $1\,dm^3 = 1\,dm \times 1\,dm \times 1\,dm$
  • $1\,dm^3 = 10\,cm \times 10\,cm \times 10\,cm = 1,000\,cm^3$
  • $1\,dm^3 = 1\text{ litre}$

Vessels for Measuring Liquid Volume

• Types of Vessels: Two primary tools are used:
  1. Measuring cylinder
  2. Measuring beaker

Measuring Cylinder

• Physical Description: It is a cylinder typically made of glass or plastic with a cross-sectional area of approximately $10\,cm^2$.
• Graduation: The length is approximately $10\,cm$, graduated in $cm^3$ (or $mL$). The zero mark is located at the bottom, and the highest mark ($100$) is at the top.
• Capacity: Standard capacity is $100\,cm^3$ (or $100\,mL$).
• Applications:
  • Commonly used in laboratories to measure liquid volumes.
  • Used to find the volume of irregular objects through the displacement of water or liquid.
• Other Sizes: Larger measuring cylinders are available in capacities such as $200\,mL$ and $500\,mL$.

Measuring Beaker

• Purpose: Used to measure a specific, fixed volume of a liquid, such as milk, oil, or lubricating oil.
• Available Capacities: Beakers come in various fixed sizes: $50\,mL$, $100\,mL$, $200\,mL$, $500\,mL$, and $1000\,mL$.

Procedures for Measuring Liquid Volume

Using a Measuring Cylinder

1. Take a measuring cylinder, wash it thoroughly with water, and dry it.
2. Place the cylinder on a flat, level surface.
3. Pour the liquid into the cylinder gently to ensure no splashing occurs.
4. Wait for the liquid to become stationary.
5. Observe the meniscus: The upper surface of the water is curved when stationary. Measurements should be taken based on the appropriate level of the meniscus.

Using a Measuring Beaker

• This method is used when a specific fixed volume needs to be extracted from a large volume.
• Example: Measuring $500\,mL$ of milk from a bucket.
• Process: Select a measuring beaker with the exact capacity required ($500\,mL$) and fill it from the larger container.

Measurement of Regular and Irregular Objects

Volume of Regular Objects

• The volume of regular objects is determined by measuring their dimensions (length, breadth, height, or radius) and applying formulas:
  • Volume of a Cube: $(\text{one side})^3$
  • Volume of a Cuboid: $\text{length} \times \text{breadth} \times \text{height}$
  • Volume of a Sphere: $V = \frac{4}{3} \times \pi \times (\text{radius})^3$ (Transcript indicates proportionality to $r^3$).
  • Volume of a Cylinder: $\pi \times (\text{radius})^2 \times \text{height}$
  • Volume of a Cone: $V = \frac{1}{3} \times \pi \times (\text{radius})^2 \times \text{height}$ (Transcript indicates proportionality to $r^2 \times h$).

Volume of Irregular Objects

• Method: The Displacement Method using a measuring cylinder.
• Principle: The volume of an irregular solid is equal to the volume of the liquid it displaces when completely immersed.

Area

• Definition: The surface occupied by an object is called its area.
• S.I. Unit: Square metre, denoted as $m^2$.
  • $1\,m^2 = 1\,m \times 1\,m$
• Large Units:
  • Are: The area of a square with each side measuring $10\,m$.
  • $1\text{ are} = 10\,m \times 10\,m = 100\,m^2$
  • Hectare: The area of a square with each side measuring $100\,m$.
  • $1\text{ hectare} = 100\,m \times 100\,m = 10,000\,m^2$
  • Square Kilometre: The area of a square with each side measuring $1\,km$.
  • $1\,km^2 = 1\,km \times 1\,km = 1,000,000\,m^2 = 10^6\,m^2$
• Smaller Units (for objects like pencils or rubbers):
  • Square Centimetre ($cm^2$): $1\,cm^2 = 1\,cm \times 1\,cm = 10^{-4}\,m^2$
  • Square Millimetre ($mm^2$): $1\,mm^2 = 1\,mm \times 1\,mm = 10^{-6}\,m^2$

Area of Regular Objects

• Calculated by measuring two dimensions:
  • Area of a Square: $(\text{one side})^2$
  • Area of a Rectangle: $\text{length} \times \text{breadth}$
  • Area of a Circle: $\pi \times r^2$
  • Surface Area of a Cylinder: $2\pi \times \text{radius} \times \text{length}$
  • Surface Area of a Sphere: $4\pi \times (\text{radius})^2$

Area of Irregular Objects

• Method: Using graph paper where each square has a side of $1\,cm$, meaning each square represents an area of $1\,cm^2$.
• Formula: $\text{Approximate Area} = (\text{No. of complete squares} + \text{No. of half or more than half incomplete squares}) \times \text{Area of one square}$
• Calculation Example: For an object covering $4$ complete squares and $4$ half or more squares:
  • $A = (4 + 4) \times 1\,cm^2 = 8\,cm^2$

Density

Fundamental Concepts

• Every body possesses a certain mass and a definite volume.
• Equal Masses of Different Substances: Occupy different volumes.
  • Example: $1\,kg$ of sugar occupies more volume than $1\,kg$ of iron; therefore, iron is denser than sugar.
• Equal Volumes of Different Substances: Have different masses.
  • Example: An iron cube and an aluminium cube of the same size (equal volume) will differ in mass. The mass of the iron is greater.
• Comparative Density Examples:
  • Aluminium is denser than glass (mass of aluminium cube > identical glass cube).
  • Glass is denser than wood (mass of glass cube > identical wooden cube).
  • Milk is denser than water (a certain volume of milk has more mass than an equal volume of water).

Definition and Formula

• Density ($d$): Defined as the mass per unit volume of a substance.
• Formula: $d = \frac{M}{V}$
• Calculated Example (Water):
  • Given: $M = 1\,g$, $V = 1\,cm^3$
  • $\text{Density of water} = \frac{1\,g}{1\,cm^3} = 1\,g\,cm^{-3}$
• Properties: The density of a substance does not change with changes in its shape or size.

Units of Density

• S.I. Unit: Mass is in Kilograms ($kg$) and Volume is in Cubic metres ($m^3$), so Density is measured in $kg\,m^{-3}$.
• C.G.S Unit: Mass is in Grams ($g$) and Volume is in Cubic centimetres ($cm^3$), so Density is measured in $g\,cm^{-3}$.
• Relationship between $kg\,m^{-3}$ and $g\,cm^{-3}$:
  • $1\,kg = 1000\,g$ or $1\,g = \frac{1}{1000}\,kg$
  • $1\,m^3 = (100\,cm)^3 = 1,000,000\,cm^3$ or $1\,cm^3 = \frac{1}{1,000,000}\,m^3$
  • $1\,g\,cm^{-3} = \frac{10^{-3}\,kg}{10^{-6}\,m^3} = 1000\,kg\,m^{-3}$

Temperature and Density

• Generally, the density of solids, liquids, and gases decreases as temperature increases because substances expand when heated.
• Anomalous Expansion of Water:
  • Water contracts when heated from $0^\circ C$ to $4^\circ C$.
  • Water expands when heated above $4^\circ C$.
  • The density of water is at its maximum at $4^\circ C$.
  • Density decreases whether the water is cooled from $4^\circ C$ to $0^\circ C$ or heated above $4^\circ C$.

Determination of Density of Regular Solids

1. Measure the Mass ($M$) of the solid using a beam balance.
2. Measure the dimensions (length, breadth, height) using a metre ruler.
3. Calculate Volume: $V = \text{length} \times \text{breadth} \times \text{height}$.
4. Apply the formula: $d = \frac{M}{V}$.

Determination of Density of Irregular Solids (Stone/Coin)

1. Measure the mass ($M$) of the solid using a beam balance (in grams).
2. Use the displacement method for volume:
   • Partially fill a measuring cylinder with water.
   • Record initial volume level ($V_1$).
   • Tie the solid with a thread and immerse it gently in the cylinder.
   • Record the new volume level ($V_2$) in $mL$.
3. Calculate the volume of the solid: $V = V_2 - V_1\,cm^3$ (since $1\,mL = 1\,cm^3$).
4. Calculate density: $d = \frac{M}{V_2 - V_1}\,g\,cm^{-3}$.

Determination of Density of a Liquid (e.g., Milk)

1. Measure the mass of an empty beaker using a beam balance ($M_1$).
2. Use a measuring cylinder to measure a specific volume ($V$) of the liquid (e.g., $50\,mL$ of milk, which is $50\,cm^3$).
3. Pour the liquid into the empty beaker and measure the mass again ($M_2$).
4. Calculate the mass of the liquid: $M = M_2 - M_1$.
5. Calculate density: $d = \frac{M}{V}$.

Speed

• Definition of Distance: When a body is in motion, the length of the path travelled in a certain time is the distance moved.
• Unit of Distance: Metre ($m$).
• Understanding Speed: Speed is measured to determine how fast or slow an object is moving by comparing distance travelled in a specific time interval.
  • Example: A car travels more distance than a bullock cart in the same time interval, meaning the car moves faster.
• Definition of Speed: Speed is the distance travelled divided by time taken.
• Variable Representation: Denoted by $v$.
• Formula: $v = \frac{d}{t}$
• Units:
  • S.I. Unit: $m\,s^{-1}$
  • Other Units: $km\,h^{-1}$
• Conversion Relationships:
  • $1\,km\,h^{-1} = \frac{1000\,m}{3600\,s} = \frac{5}{18}\,m\,s^{-1}$
  • $1\,m\,s^{-1} = 3.6\,km\,h^{-1}$