ICSE Class 8 Physics Physical Quantities and Measurement Notes PDF Download

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Physical Quantities and Measurement Notes ICSE Class 8

Introduction to Density

• Every body has:
  ⦿ A certain mass
  ⦿ A definite volume
• Different substances may have:
  ⦿ Equal masses but different volumes
  ⦿ Equal volumes but different masses
• To compare substances, we use density.

Definition of Density

Density of a substance is the mass per unit volume.

Density \(=\frac{\operatorname{Mass}}{Volume}\)

Meaning of Density

• A substance with high density has particles packed closely together.

• A substance with low density has particles loosely packed.

Examples

1. Equal Mass but Different Volume
1 kg cotton occupies more space than 1 kg iron.
Reason: Cotton is less dense.

2. Equal Volume but Different Mass
1 cm³ iron has more mass than 1 cm³ wood.
Reason: Iron is denser.

Units of Density

• ​S.I. Unit: kg m^–3 (kilogram per cubic metre)
• ​C.G.S. Unit: g cm^–3 (gram per cubic centimetre)

Relation Between Units

• 1 g cm^–3 = 1000 kg m^–3
• 1 kg m^–3 = 10^–3 g cm^–3

Examples of Density

• Density of water = 1 g cm^–3
• Density of iron = 7.8 g cm^–3
• Density of milk = 1.03 g cm^–3

***Note
The density of brass is 8.4 g cm^–3 means 1 cm³ of brass has a mass of 8.4 g.

Important Facts

1. Density does not depend on shape
If shape changes, density remains same.

2. Effect of Temperature
Most substances expand on heating.
So:
⦿ Volume increases
⦿ Density decreases
On cooling:
⦿ Volume decreases
⦿ Density increases

Exception: Water

• Water contracts from 0°C to 4°C
• Hence density increases.
• Water has maximum density at 4°C
  1000 kg m^–3

Determination of Density of a Regular Solid

A regular solid has a definite shape such as cube, cuboid, cylinder or sphere.

Steps:

Step 1: Measure Mass
Use a beam balance to measure mass (M).

Step 2: Measure Volume
Use formulas according to shape:

• Cube: V = (side)³
• ​Cuboid: V = length × breadth × height
• ​Sphere: V =  × π × (radius)³
• Cylinder: V = π × (radius)² × h

Step 3: Calculate Density

Density \(=\frac{\operatorname{Mass}}{Volume}\)

Example of Regular Solid

• Mass of iron cube = 210 g
• Side = 3 cm
• Volume, V = 3³ = 27 cm³
• Density \(=\frac{\operatorname{Mass}}{Volume}=\frac{210}{27}\ =\) 7.78 gm cm^–3

Determination of Density of an Irregular Solid

Irregular solids do not have fixed geometrical shape.

Examples:

• Stone
• Coin
• Metal piece

Use water displacement method.

Steps:

1. Measure mass
Let mass = M

2. Take water in measuring cylinder
Initial level = V₁

3. Put solid completely in water
Final level = V₂

4. Volume of solid
V = V₂ –V₁

5. Density
\(d=\frac{M}{V}\)

Eureka Can Method

1. Fill Eureka can till overflow stops.
2. Put solid inside.
3. Collect overflow water.
4. Measure collected water volume.

That volume = volume of solid.

Determination of Density of a Liquid

Steps:

1. Take a measuring cylinder and measure a known volume of liquid, say V.
2. Measure the mass of empty cylinder = m₁.
3. Measure the mass of cylinder with liquid = m₂.
4. Mass of liquid = m₂ – m₁.
5. Density of liquid = \(\frac{m_2\ -\ m_1}{V}\)

Example of Liquid

• Mass of empty beaker = 20 g
• Mass of beaker + milk = 71.5 g
• Volume of milk, V= 50 cm³

Mass of milk, M = 71.5 – 20 = 51.5 g

Density, d  \(=\frac{M}{V}=\frac{71.5}{51.5}=\) 1.03 g cm^–3

Density Bottle

• A density bottle is used to determine density or relative density of liquids accurately.
• Usually available in 25 mL or 50 mL capacity.

Method:

1. Measure mass of empty bottle = m₁
2. Fill with water and measure mass = m₂
3. Fill with given liquid and measure mass = m₃
4. Mass of equal volume of water = m₂ − m₁
5. Mass of equal volume of liquid = m₃ – m₁

∴ Density of liquid \(=\ \frac{m_3\ -\ m_1}{m_2\ -\ m_1}\)

Then density can be calculated.

Relative Density

Relative density is the ratio of density of a substance to density of water.

R. D. \(=\frac{Density\ of\ \operatorname{substance}}{Density\ of\ water}\)

Since density of water = 1 g cm^–3

Relative density = numerical value of density in g cm^–3.

Example:

If density of iron = 7.8 g cm^–3

Then relative density = \(\frac{7.8}{1}\)  = 7.8

Unit of Relative Density

Relative density has no unit because it is a ratio of two similar quantities. 

***Note
The statement Relative density of aluminium is 2.7 means aluminium is 2.7 times as dense as water.

• If the Relative Density of an object is greater than 1, it will sink in water. If it is less than 1, it will float.

Density and Relative Density of Some Common Substances

Differences between density and relative density:

Density in Different States of Matter

For most substances:

• Density of solid > density of liquid > density of gas
• Exception: Water

Ice density = 0.917 g cm^–3

Water density = 1 g cm^–3 Therefore, ice floats on water.

Floating and Sinking

When a body is placed in liquid:

• Some objects float.
• Some objects sink.

Examples:

• Cork floats on water.
• Iron nail sinks in water.

Reason

• If density of body < density of liquid
  Object floats.

• If density of body > density of liquid
  Object sinks.

Principle of Floatation

When a body is completely or partially immersed in liquid, two forces act on it.

Force 1: Weight (W)

• Acts vertically downward
• Tends to sink the body

Force 2: Buoyant Force (F_B)

• Acts vertically upward
• Also called upthrust

Cases of Floating and Sinking

Case 1: Weight > Buoyant Force

• W > FB
• Resultant force acts downward.
• The body sinks to the bottom.
• This happens when:
  Density of body > density of liquid

Case 2: Weight = Buoyant Force

• W = F_B
• Resultant force = zero
• The body floats just below the surface.
• This happens when:
  Density of body = density of liquid

Case 3: Weight < Buoyant Force

• W < FB
• Resultant force acts upward.
• The body floats partially above the surface.
• This happens when:
  Density of body < density of liquid

Law of Floatation

A floating body displaces a liquid whose weight is equal to the weight of the body.
Weight of displaced liquid = weight of body
This is called Law of Floatation.

Applications of Floatation

• Iron Ships: An iron needle is solid and has density greater than water, so it sinks.

• A ship is hollow and contains air, so its average density becomes less than water. Therefore it floats.

• It is easier to swim in sea water than in river water because sea water contains dissolved salts and is denser than river water. Therefore, sea water exerts greater buoyant force, making swimming easier.

• Submarines: A submarine is a vessel that can travel under water.

• To dive: tanks are filled with water, increasing density, so it sinks.

• To rise: water is forced out and tanks filled with air, decreasing density, so it floats upward.

• Icebergs: Most part of an iceberg remains below the water surface because ice is only slightly less dense than sea water.

• Ships may collide with the hidden underwater portion, making icebergs dangerous.

• Hot Air Balloons: Hydrogen or Helium gases are less dense than air, creating an upward buoyant force that lifts the balloon.

• Whales: They use an organ called a swim bladder. By filling it with air, they decrease their density to rise to the surface.

ICSE Class 8 Physics Physical Quantities and Measurement Notes PDF Download

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ICSE Class 8 Physics Notes

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