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Physical Quantities and Measurement
ICSE Class 7 Physics • Chapter 1 • Detailed Master Notes
Chapter Overview
Physics relies heavily on exact measurements. In this chapter, we explore how to measure the Volume of regular and irregular solids, the Area of surfaces, and introduce the fundamental concept of Density, which determines whether objects float or sink.
1.1 Measurement of Volume
Volume: The space occupied by an object is called its volume. The Standard International (S.I.) unit of volume is strictly the cubic metre ($m^3$).
Units of Volume and Capacity
- Liquids: Usually measured in Litres ($L$) or millilitres ($mL$).
- Conversion Rule:
$1\text{ Litre} = 1000\text{ mL}$
$1\text{ mL} = 1\text{ cm}^3$
$1\text{ m}^3 = 1000\text{ Litres}$
Measuring Volume of Regular Solids
Regular solids have a specific mathematical shape. We measure their dimensions and apply the standard mathematical formula:
| Solid Shape | Volume Formula |
|---|---|
| Cube | $Volume = \text{side}^3$ |
| Cuboid | $Volume = l \times b \times h$ |
| Cylinder | $Volume = \pi r^2 h$ |
| Sphere | $Volume = \frac{4}{3} \pi r^3$ |
Measuring Volume of Irregular Solids
Irregular solids have no defined shape (like a stone). We use the Water Displacement Method utilizing a measuring cylinder.
- Fill a measuring cylinder partially with water and carefully note the initial volume ($V_1$).
- Tie the irregular solid with a strong thread and gently lower it completely into the water.
- Note the new, higher water level reading ($V_2$).
- Volume of Solid = $V_2 - V_1$
AI Image Prompt: A clean 3D educational illustration showing a measuring cylinder filled with blue water and an irregular grey stone submerged in it, demonstrating the $V_2 - V_1$ displacement method clearly with precise red scientific arrows.
1.2 Measurement of Area
Area: The amount of flat 2D surface enclosed within the boundary of a closed figure. The S.I. unit is the square metre ($m^2$).
Area of Irregular Shapes
To measure the area of an irregular boundary like a heavy tree leaf:
- Place it on graph paper and trace its boundary.
- Count the total full squares inside the outline.
- Count the squares that are half or more than half inside the boundary.
- Total area = $(Full \text{ squares} + \text{Half or more squares}) \times (\text{Area of 1 square})$. Ignore squares that are completely less than half.
1.3 Density
Why does a heavy piece of wood completely float freely on water, while a small iron nail firmly sinks immediately? This happens due to totally different densities.
Density: The density of a substance is defined as its mass per unit volume. It tells us how tightly matter is packed together.
$\text{Density } (d) = \frac{\text{Mass } (M)}{\text{Volume } (V)}$
- S.I. Unit: $kg/m^3$ (kilograms per cubic metre).
- C.G.S. Unit: $g/cm^3$ (grams per cubic centimetre).
- Conversion: $1\text{ g/cm}^3 = 1000\text{ kg/m}^3$.
Principle of Floatation:
- If the density of an object is less than the density of a liquid, it will float.
- If the density of an object is greater than the density of a liquid, it will sink.
- For example, the density of water is $1\text{ g/cm}^3$. An iron nail has a density of about $7.8\text{ g/cm}^3$, so it sinks. Cork has a density of $0.24\text{ g/cm}^3$, so it floats.
AI Image Prompt: A vibrant visual of a glass beaker filled with water. A heavy iron nail is resting at the bottom (sunk), while a light wooden block and a cork are floating beautifully on the surface. Add labels showing their respective densities compared to water (1 g/cm3).
1.4 Speed
Speed: Speed is the total distance travelled by a body per unit of time. It tells us how fast an object is moving.
$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
- S.I. Unit: Metres per second ($m/s$).
- Common Unit: Kilometres per hour ($km/h$), often used for vehicles like cars and trains.
- Conversion Trick:
To convert $km/h$ to $m/s$: Multiply by $\frac{5}{18}$.
To convert $m/s$ to $km/h$: Multiply by $\frac{18}{5}$.
Uniform vs Non-Uniform Speed:
- Uniform Speed: When a body travels equal distances in equal intervals of time. (e.g., A train moving at exactly $60\text{ km/h}$ on a straight track).
- Non-Uniform Speed: When a body travels unequal distances in equal intervals of time. (e.g., A car moving through a crowded city street).
Q1. A block of wood has a mass of $50\text{ g}$ and a volume of $100\text{ cm}^3$. Calculate its density and state if it will float in water.
Ans: Density = $\frac{Mass}{Volume} = \frac{50}{100} = 0.5\text{ g/cm}^3$. Since $0.5$ is less than $1$ (density of water), it will float.
Q2. Convert $54\text{ km/h}$ into $m/s$.
Ans: $54 \times \frac{5}{18} = 3 \times 5 = 15\text{ m/s}$.