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Physical Quantities & Measurement
ICSE Class 8 Physics • Chapter 2 (Detailed Master Notes)
Chapter Overview
Physics is the science of exact measurement. To study nature, we must quantify it. How heavy is it? How long is it? How dense is it? In this chapter, we will master the concept of Density—the "compactness" of an object—and understand why a massive steel ship floats while a tiny steel nail sinks in the exact same water.
2.1 Understanding Density
If you pick up a block of iron and an identical-sized block of wood, the iron feels much heavier. Why? Because the iron molecules are packed much tighter together. Iron has a higher density than wood.
Density ($d$) is defined as the mass of a substance per unit of its volume.
Mathematically, it tells us how tightly matter is packed within a specific given space.
Formula for Density
$Density = \frac{Mass}{Volume}$ or $d = \frac{m}{v}$
Units of Density:
- S.I. System (Standard International): Mass is in kilograms ($kg$), Volume is in cubic meters ($m^3$). Therefore, S.I. unit of density is $kg/m^3$ (or $kg \cdot m^{-3}$).
- C.G.S. System: Mass is in grams ($g$), Volume is in cubic centimeters ($cm^3$ or $cc$). Therefore, C.G.S. unit of density is $g/cm^3$.
AI Image Prompt: A 3D educational illustration comparing two identical transparent glass cubes of exactly the same volume. The left cube (low density) contains only a few scattered floating red spheres. The right cube (high density) is packed entirely full with hundreds of tightly arranged red spheres. Label the left "Low Density" and the right "High Density".
Relationship between $kg/m^3$ and $g/cm^3$:
This is a critical conversion factor commonly asked in numericals:
$1 \text{ } g/cm^3 = 1000 \text{ } kg/m^3$
Example: The density of pure water is $1 \text{ } g/cm^3$. In S.I. units, it is exactly $1000 \text{ } kg/m^3$.
2.2 Measuring the Density of Solids
A. Regular Solids
A regular solid has a fixed, mathematically calculable shape (like a cube, cuboid, or sphere).
- Find the Mass ($m$) using a physical balance or electronic weighing scale.
- Find the Volume ($v$) by measuring the dimensions (length, breadth, height) with a
ruler and applying mathematical formulas.
(e.g., Volume of Cuboid = $l \times b \times h$). - Apply the formula: $d = m/v$.
B. Irregular Solids
An irregular solid has no fixed shape (like a random stone), so we cannot use a ruler to find its volume. We use a Measuring Cylinder via the water displacement method.
- Find the Mass ($m$) using a beam balance.
- Fill a measuring cylinder partially with pure water. Note the initial volume level ($V_1$).
- Tie the irregular solid to a thin string and lower it completely into the water without splashing.
- The water level will forcibly rise. Note the final exact new volume level on the cylinder ($V_2$).
- The Volume ($v$) of the solid is solely the difference in water levels: $v = V_2 - V_1$.
- Calculate Density: $d = \frac{m}{V_2 - V_1}$.
2.3 Relative Density (Specific Gravity)
Sometimes, instead of absolute density, we just want to compare how heavy a substance is compared to water. This is called Relative Density (R.D.).
Relative Density is the exact ratio of the density of a substance to the precise density of water at exactly $4^\circ C$.
Formula for Relative Density
$Relative\ Density = \frac{Density\ of\ Substance}{Density\ of\ Water\ at\ 4^\circ C}$
CRITICAL FACT: Because Relative Density is a strict ratio of two similar quantities (Density divided by Density), the units completely cancel out. Therefore, Relative Density has NO unit. It is simply a pure number.
Interpretation: If the R.D. of iron is 7.8, it simply means a given volume of iron is 7.8 times heavier than an equal volume of water.
AI Image Prompt: A vibrant scientific beaker filled with clear blue water. Inside the beaker, three objects are shown interacting with the water: a piece of cork floating high on the surface, a block of wood floating partially submerged, and a heavy iron bolt resting deep at the very bottom. Clean white background.
2.4 Principle of Floatation
Why do things float or sink? It depends entirely on their density compared to the liquid (usually water) they are placed in.
- Sinking: If the density of an object is greater than the density of the liquid, it will definitively sink to the bottom. (e.g., A stone in water).
- Floating: If the density of an object is less than the density of the liquid, it will confidently float on the surface. (e.g., Cork or wood in water).
- Suspended: If the density of the object is exactly equal to the density of the liquid, it will remain suspended anywhere within the liquid without floating up or sinking down.
Q1. A solid has a mass of 500g and occupies a volume of $100 cm^3$. Calculate its density and state if it will float or sink in water.
Answer:
Mass ($m$) = $500\text{ g}$
Volume ($v$) = $100\text{ cm}^3$
$Density = m / v = 500 / 100 = 5\text{ g/cm}^3$
Since the density of water is $1\text{ g/cm}^3$, the solid's density ($5\text{ g/cm}^3$) is far greater.
Therefore, the robust solid will decidedly sink.
Q2. Why does a massive heavy steel ship miraculously float on the ocean, but a tiny solid steel nail quickly sinks?
Answer: A steel nail is completely solid, so its average density is entirely that of steel (which is higher than water), causing it to effectively sink. A massive ship is intelligently uniquely built with a hollow interior containing vast empty spaces filled with air. This drastically intelligently significantly reduces the average density of the whole entire whole ship explicitly to be strictly successfully less than the density of seawater, allowing it to proudly safely effortlessly float.