Chapter 3 – Matter Structure and Properties | Chapter Solution Class 9

Pressure is the normal force exerted by a fluid on any surface in contact with it per unit area.

The S.I. unit of pressure is Newton per square meter (Nm⁻²), also called Pascal (Pa).

he normal force exerted by a fluid on any surface in contact with it is called thrust.

The S.I. unit of thrust is Newton (N).

Pressure = Thrust / Area.

The two forces acting on an object immersed in a fluid are:

1. Weight of the object (W) acting downward.
2. Upthrust (Buoyant force) exerted by the fluid acting upward.

The upward force exerted by a fluid on a body partially or fully immersed in it is called upthrust or buoyant force.

Upthrust depends on:

1. Volume of the body immersed in the fluid.
2. Density of the fluid.
3. Acceleration due to gravity (g).

Archimedes’ principle states that a body partially or fully immersed in a fluid at rest appears to lose a part of its weight equal to the weight of the fluid displaced.

Relative density of a substance is the ratio of the density of the substance to the density of pure water at 4°C. It has no unit.

Density of a substance is its mass per unit volume.

Density = Mass / Volume

The S.I. unit of density is kg/m³.

The forces acting on a body immersed in a liquid are:

1. Weight of the body acting downward.
2. Upthrust exerted by the liquid acting upward.

The atmosphere is the layer of air that surrounds the Earth and extends up to about 500 km above the surface.

Barometer.

Normal atmospheric pressure is 760 mm of mercury column.

A siphon is a device used for transferring liquid from one vessel to another without disturbing the whole volume of the liquid or pouring it.

The S.I. unit of surface tension is Nm⁻¹.

Surface tension is a scalar quantity because it has magnitude but no direction.

Streamlines are the paths of fluid particles in steady flow, where each particle follows the exact path of its predecessor.

Bernoulli’s theorem is based on the principle of conservation of energy.

Stress is the restoring force developed per unit area of a body when a deforming force is applied.

Stress = Force / Area.

Strain is the ratio of change in length, volume, or shape of a body to its original configuration.

It has no unit as it is a pure number.

The S.I. unit of stress is Nm⁻² or Pascal (Pa).

Hooke’s Law states that within the elastic limit, stress is directly proportional to strain.

Stress / Strain = a constant.

Examples of ductile materials:

1. Copper
2. Aluminium

Examples of brittle solids:

1. Glass
2. Cast Iron

Bridges are designed to withstand heavy loads and traffic without bending beyond their elastic limit.

Consider a horizontal area A containing a point P at a depth h below the surface of a liquid of density ρ.

Volume of the liquid column = A × h

Mass of the liquid column = A × h × ρ

Weight of the liquid column = A × h × ρ × g

Pressure at point P is given by:

P = Force / Area = (A × h × ρ × g) / A

P = hρg

The characteristics of liquid pressure are:

1. Pressure at all points in a liquid at the same level is the same in all directions.
2. Liquid pressure depends on the height of the liquid column above the point.
3. Liquid pressure acts equally in all directions at a given depth.
4. The total pressure at a depth includes both atmospheric pressure and liquid pressure.
5. Liquid pressure is a scalar quantity.

Take several interconnected vessels of different shapes and fill them with liquid. It is observed that the level of the liquid in all vessels remains the same, regardless of their shape. This proves that a liquid always finds its own level.

Application:

This principle is used in water supply systems, where water pumped to overhead tanks distributes evenly in different connected pipelines.

A barometer is used to measure atmospheric pressure. It consists of a long glass tube filled with mercury and inverted into a mercury-filled container. The height of the mercury column (760 mm at sea level) indicates the atmospheric pressure. The Fortin’s barometer is an improved version used for precise measurements.

A siphon is a device used for transferring liquid from one container to another without disturbing the liquid volume. It consists of a bent tube with one end in a higher container and the other in a lower container.

Conditions for working of a siphon:

1. The liquid in the higher container must be at a higher level than in the lower container.
2. The flow occurs under atmospheric pressure.
3. A siphon does not work in a vacuum.

Archimedes’ principle: A body immersed in a fluid experiences an apparent loss in weight equal to the weight of the fluid displaced.

Proof:

• Take a stone and measure its weight W₁ in air.
• Immerse the stone in water and measure its new weight W₂.
• The apparent loss in weight W₁ – W₂ is equal to the weight of displaced water.
  This verifies Archimedes’ principle.

Density is the mass per unit volume of a substance. Density = Mass / Volume. SI unit is kg/m³.

Relative density is the ratio of the density of a substance to the density of pure water at 4°C. It has no unit.

Surface tension is the property of a liquid by which its surface behaves like a stretched membrane to minimize its area.

• S.I. unit: Nm⁻¹
• Nature: It is a scalar quantity as it has magnitude but no specific direction.

Streamline flow: A fluid flow where every particle follows the same path as its predecessor. Example: Water flowing in a smooth pipe.

Turbulent flow: A fluid flow where particles move in random and chaotic paths. Example: Water flow in a river.

Terminal velocity is the constant velocity a falling object attains when the downward force due to gravity equals the upward force due to viscosity and buoyancy.

Factors affecting terminal velocity:

1. Radius of the ball
2. Density of the ball
3. Density of the liquid
4. Viscosity of the liquid

As water falls, its velocity increases due to gravity. According to the equation of continuity A × v = constant, when velocity increases, the cross-sectional area decreases. This causes the stream to become narrower as it goes down.

Bernoulli’s theorem: The total energy (pressure energy + kinetic energy + potential energy) per unit mass remains constant for an ideal liquid in streamline flow.

Application:

Aeroplane lift: The curved shape of an aerofoil increases airspeed above the wing, reducing pressure. The higher pressure below lifts the plane.

Elasticity is the property of a material by which it resists deformation and regains its original shape when the deforming force is removed.

Factors affecting elasticity:

1. Nature of material
2. Temperature
3. Presence of impurities
4. Method of processing (rolling, hammering, etc.)

Hooke’s Law: Within the elastic limit, stress is directly proportional to strain.

Elastic Modulus: The ratio of stress to strain. It measures the stiffness of a material.

Beyond the elastic limit, a material no longer returns to its original shape. It undergoes plastic deformation, where it permanently changes shape.

Examples:

1. Ductility: Wire stretches into thin sheets (e.g., copper).
2. Brittleness: Material breaks when stress is applied (e.g., glass).
3. Malleability: Can be hammered into sheets (e.g., gold).

Bridges and buildings are designed to withstand forces without bending beyond their elastic limit.

Cranes and metallic ropes are designed with strong materials that do not exceed elasticity.

Car shock absorbers use elasticity to absorb road shocks.

According to Bernoulli’s theorem, when a fast-moving train passes, the air between the train and a person moves at high speed, reducing pressure. The higher atmospheric pressure on the other side pushes the person toward the train, making it dangerous.

An atomiser (like a perfume sprayer) works on Bernoulli’s principle. When air is blown rapidly over a tube, the pressure inside decreases. The liquid rises due to the pressure difference and is expelled as fine droplets.

Given, diameter of vessel = 28 cm

Radius (r) = \frac{28}{2} = 14 cm = 0.14 m

Volume of mercury = 30.8 L = 30.8 × 10⁻³ m³

Density of mercury = Relative Density × Density of water

ρ = 13.6 × 1000 = 13600 kg/m³

Pressure due to mercury column:

P = hρg

h = \frac{\text{Volume}}{\text{Area}} = \frac{30.8 \times 10^{-3}}{\pi (0.14)^2}

h = 0.5 m

P = 0.5 × 13600 × 9.8

P = 66.64 × 10³ Nm⁻²

Given, mass (m) = 1 kg,

acceleration due to gravity (g) = 10 ms⁻²

Weight of block (W) = mg = 1 × 10 = 10 N

Area of contact (A) = side²

= (2 × 10⁻²)²

= 4 × 10⁻⁴ m²

Pressure (P) = \frac{F}{A} = \frac{10}{4 \times 10^{-4}}

P = 2.5 × 10⁴ Pa

Given, side of the cubical tank l = 2 m

Area of bottom A = l² = (2 × 2) = 4 m²

Pressure at bottom P = hρg

= 2 × 1000 × 9.8

= 19600 N/m²

Force on the bottom F = P × A

= 19600 × 4 = 78400 N

In kg-wt, F = \frac{78400}{9.8}

= 8000 kg-wt

Density of iron (ρ) = Relative Density × Density of water

ρ = 7.874 × 1000

ρ = 7874 kg/m³

Given, mass of bottle (m) = 500 g,

volume (V) = 450 cm³

Density of bottle ρ = \frac{m}{V}</p> <p>= \frac{500}{450}

= 1.11 g/cm³

Since the density of the bottle (1.11 g/cm³) is greater than that of water (1 g/cm³), the bottle will sink.

Mass of displaced water = Density × Volume

= 1 × 450 = 450 g

Pressure P = \frac{F}{A}

Case 1: 100 kg mass on 10 m²

P₁ = \frac{100 \times 9.8}{10}

= 98 Pa

Case 2: 50 kg mass on 4 m²

P₂ = \frac{50 \times 9.8}{4}

= 122.5 Pa

Since P₂ > P₁, the second case exerts more pressure.

Volume of block (V) = 2 × 0.25 × 0.10

= 0.05 m³

Density of wood (ρ) = 0.6 × 1000 = 600 kg/m³

Mass (m) = ρ × V

= 600 × 0.05

= 30 kg

L = 250 cm,

d = 1 mm = 0.1 cm,

Y = 20 × 10¹¹ dyne/cm²

Force F = mg = 8 × 980 dyne

Area (A) = \frac{\pi d^2}{4} = \frac{\pi (0.1)^2}{4}

Elongation (ΔL) = \frac{F L}{A Y}

= 0.125 cm

Given,

L = 100 cm,

d = 0.1 cm,

Y = 1 × 10¹² dyne/cm²

Force (F) = mg = 2 × 980 dyne

Area (A) = \frac{\pi d^2}{4}

Elongation (ΔL) = \frac{F L}{A Y} = 0.025 cm

L = 628 cm,

ΔL = 0.1 cm,

d = 0.2 cm

Y = 2 × 10¹² dyne/cm²,

g = 980 cm/s²

Area (A) = \frac{\pi d^2}{4}

Load (m) = \frac{A Y \Delta L}{L g}

= Required Load (kg)

1. thrust
2. finds
3. barometer
4. atmospheric
5. buoyancy
6. number
7. scalar
8. temperature
9. energy
10. increased

False

Explanation: Liquid pressure increases with increasing depth, not decreasing depth. This is because pressure at a point in a liquid is given by p=hρg, where h is the depth, ρ is the density, and g is acceleration due to gravity.

True

Explanation: If the density of a solid body is less than the density of the liquid, the upthrust acting on it is greater than its weight, causing it to float.

False

Explanation: A siphon works due to atmospheric pressure. In a vacuum, there is no atmospheric pressure to push the liquid up, so a siphon cannot function.

True

Explanation: The surface tension of a liquid decreases with an increase in temperature because the cohesive forces between the liquid molecules weaken as temperature rises.

False

Explanation: Gases are compressible and their volume changes significantly with pressure, especially at high pressures.

False

Explanation: Terminal velocity depends on the size of the ball, as it is influenced by factors such as drag force and buoyancy, which are affected by the object’s radius and shape.

True

Explanation: The shape of an aerofoil is designed such that the upper surface is more curved than the lower surface, creating a pressure difference that provides lift.

True

Explanation: As temperature increases, the kinetic energy of the molecules increases, reducing intermolecular forces and thereby decreasing the elasticity of the material.

False

Explanation: The unit of longitudinal strain is dimensionless (it has no unit) because it is the ratio of change in length to the original length.

True

Explanation: Glass is a brittle material because it breaks without significant deformation when subjected to stress.

(a) pascal

Explanation: Pascal (Pa) is the SI unit of pressure, defined as force per unit area (N/m²).

(d) all of these

Explanation: Upthrust or buoyant force depends on the volume of the displaced liquid, the density of the liquid, and the acceleration due to gravity (g), as per Archimedes’ principle.

(a) float wholly immersed

Explanation: When the density of the object matches the liquid’s density, the object remains suspended in the liquid without sinking or rising.

(b) barometer

Explanation: A barometer is an instrument used to measure atmospheric pressure, usually with mercury in a tube.

(b) s = ρ/d

Explanation: Relative density is the ratio of the density of a substance to the density of water at 4°C, which is taken as a standard reference.

(d) Nm⁻¹

Explanation: Surface tension is measured as force per unit length, and its SI unit is Newton per meter (N/m).

(d) all of these

Explanation: Terminal velocity depends on the radius of the body, the density of the medium, and the viscosity of the medium, as described by Stokes’ Law.

(c) energy

Explanation: Bernoulli’s theorem states that the total mechanical energy (pressure energy, kinetic energy, and potential energy) of a flowing fluid remains constant.

(b) decreases

Explanation: As temperature increases, the intermolecular bonds weaken, reducing the elastic limit of the material.

(b) brittle

Explanation: Brittle materials break without significant deformation after crossing the elastic limit, examples include glass and cast iron.