📖 Lesson 6: Measurement of Density and Relative Density

👩🏽‍🏫 Introduction

Hello again, scientist! 👋🏽

Ever wondered why a stone sinks in water but a piece of wood floats? Or why oil floats on top of water in your soup? The answer lies in density—a concept that helps us understand how heavy things are for their size.

In this lesson, you’ll learn how to measure the density of different objects, both regular and irregular, and how to compare the density of one substance to another using relative density.

By the end, you’ll be able to do real-world experiments and solve problems like a true science pro! ⚖️💧

📘 Core Concepts

🔹 What is Density?

Density is the amount of mass packed into a given volume.

Density (𝜌)=Mass (m)Volume (V)Density (𝜌)=Volume (V)Mass (m)​

• SI Unit: kilogram per cubic metre (kg/m³)
  (or g/cm³ in smaller-scale lab work)

🔹 Examples of Densities

🔍 Key idea: Objects denser than water sink. Objects less dense float!

🔹 How to Measure Density

There are two main methods based on the object’s shape.

📏 A. Density of a Regular Object

These objects have straight edges like cubes or cylinders.

Step 1: Measure the mass using a scale.
Step 2: Measure the dimensions (length, width, height).
Step 3: Calculate volume using:

$$\text{Volume}=\text{Length}\times \text{Width}\times \text{Height}$$

Step 4: Use the formula:

Density=MassVolumeDensity=VolumeMass​

💧 B. Density of an Irregular Object

These objects don’t have regular shapes.

Step 1: Measure the mass using a balance.
Step 2: Fill a measuring cylinder with water and record the initial volume.
Step 3: Gently lower the object into the cylinder. Record the new volume.
Step 4:

$$\text{Volume}=\text{Final volume}-\text{Initial volume}$$

Step 5: Calculate density using the formula.

This is called the displacement method.

📘 What is Relative Density?

Relative Density (R.D.) compares the density of a substance to the density of water.

Relative Density=Density of substanceDensity of waterRelative Density=Density of waterDensity of substance​

Since water has a density of 1.0 g/cm³, the R.D. is just the same number without units.

👨🏽‍🔬 Real-Life Application

• Ice floats on water because its relative density is less than 1.

• Iron sinks in water because its relative density is greater than 1.

• Ships are made of steel but float because of their shape (they displace a lot of water).

🧩 Sample Problem Walkthrough

🧠 Problem 1:

A wooden block has a mass of 400 g and dimensions 20 cm × 10 cm × 2 cm. What is its density?

Step-by-step:

• Volume = 20 × 10 × 2 = 400 cm³

• Density = Mass ÷ Volume = 400 g ÷ 400 cm³ = 1.0 g/cm³

✔️ Answer: The density is 1.0 g/cm³

🧠 Problem 2:

An irregular stone has a mass of 300 g. When placed in a measuring cylinder, the water level rises from 100 cm³ to 140 cm³. Find its density and relative density.

Solution:

• Volume = 140 cm³ – 100 cm³ = 40 cm³

• Density = 300 g ÷ 40 cm³ = 7.5 g/cm³

• Relative density = 7.5 ÷ 1.0 = 7.5

✔️ Answer:

• Density = 7.5 g/cm³

• Relative density = 7.5

✍🏽 Practice Exercises

1. Fill in the Blanks

(a) Density is mass divided by __________.
(b) Relative density has __________ unit.
(c) An object floats in water if its density is __________ than water’s.

Answers:
(a) volume
(b) no
(c) less

2. Match the Instrument to Its Use

Answers:
(i) → C
(ii) → B
(iii) → A

3. Short Answer

Question: Explain why oil floats on water even though both are liquids.

Sample Answer:
Because oil has a lower density than water, so it floats on top.

🌀 Recap

Today, you learned:

• Density = Mass ÷ Volume

• Regular objects use dimension-based volume; irregular ones use displacement.

• Relative Density compares a substance’s density to that of water.

• If R.D. > 1 → sinks; if R.D. < 1 → floats.

💭 Reflection Prompt

Pick any object near you—a pen, eraser, coin, or rock.
Can you describe how you’d measure its density? What instruments would you need, and what kind of error might you encounter?

Write your response in your science journal or explain it to a classmate.