Vidya Nirman Physics - Class 9th CBSE/ICSE Comprehensive Portal

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Class 9th Physics • Chapter 1

1. Motion in One Dimension & Kinematics

Vast Theory + Derivations

1.1 Fundamental Concepts: Rest & Motion

An object is said to be in rest if its position does not change with respect to its surrounding origin/reference point over time. Conversely, an object is in motion if its position continuously changes with respect to a fixed reference frame. Rest and motion are relative terms; a person sitting inside a moving train is at rest relative to fellow passengers, but in motion relative to trees outside.

Scalar Quantities

Physical quantities that possess only magnitude and no direction.

Examples: Distance, Speed, Mass, Time, Work, Energy, Density.
Addition: Added using simple algebraic rules (e.g., $5\text{ m} + 3\text{ m} = 8\text{ m}$).

Vector Quantities

Physical quantities that require both magnitude and specific direction for complete description.

Examples: Displacement, Velocity, Acceleration, Force, Momentum.
Addition: Added using vector algebra laws (Triangle/Parallelogram law).

1.2 Distance vs Displacement (Deep Comparative Analysis)

Property	Distance ($s$)	Displacement ($\Delta x$)
Definition	Total length of actual path traversed by body.	Shortest straight line distance between initial and final position.
Quantity Type	Scalar	Vector
Possible Values	Always positive ($>0$) for a moving body.	Can be positive, zero, or negative.
Circular Motion Case	After 1 round of radius $r$: Distance $= 2\pi r$.	After 1 round: Displacement $= 0$.

1.3 Derivations of Equations of Motion (Graphical & Algebraic)

For an object moving along a straight line with uniform acceleration $a$, initial velocity $u$, final velocity $v$, time $t$, and displacement $s$:

1. First Equation of Motion ($v = u + at$)

By Definition of Acceleration: Acceleration is the rate of change of velocity per unit time.

$$a = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Time}} = \frac{v - u}{t}$$

Multiplying both sides by $t$ gives $at = v - u$. Rearranging terms:

$$v = u + at \quad \text{[Derived]}$$

2. Second Equation of Motion ($s = ut + \frac{1}{2}at^2$)

Algebraic Proof: For uniform acceleration, Average Velocity $v_{\text{avg}} = \frac{u + v}{2}$.

Total Distance $s = v_{\text{avg}} \times t = \left(\frac{u + v}{2}\right) \times t$.

Substitute $v = u + at$ into the distance equation:

$$s = \left(\frac{u + (u + at)}{2}\right) \times t = \left(\frac{2u + at}{2}\right) \times t = \left(u + \frac{1}{2}at\right) \times t$$

$$s = ut + \frac{1}{2}at^2 \quad \text{[Derived]}$$

3. Third Equation of Motion ($v^2 = u^2 + 2as$)

From the first equation $v = u + at \implies t = \frac{v - u}{a}$.

Substitute $t$ into $s = v_{\text{avg}} \times t$:

$$s = \left(\frac{v + u}{2}\right) \left(\frac{v - u}{a}\right) = \frac{v^2 - u^2}{2a}$$

Cross-multiplying $2a$ gives $2as = v^2 - u^2$. Thus:

$$v^2 = u^2 + 2as \quad \text{[Derived]}$$

1.4 Uniform Circular Motion

When an object moves along a circular path with constant speed, its direction changes continuously at every point. Since direction changes, velocity vector changes, making circular motion an accelerated motion even if magnitude of speed remains unchanged.

Speed in Circular Motion Formula:

$$v = \frac{2\pi r}{T}$$

Where $r$ = radius of circular track, $T$ = time taken for 1 complete revolution.

Solved Numerical Problem Bank

Numerical 1.1

A racing car accelerates uniformly from rest at $4\text{ m/s}^2$. What distance will it cover in $10\text{ seconds}$ after start?

Given: Initial velocity $u = 0$, acceleration $a = 4\text{ m/s}^2$, time $t = 10\text{ s}$.

Formula: $s = ut + \frac{1}{2}at^2$

Calculation: $s = (0)(10) + \frac{1}{2}(4)(10)^2 = 0 + 2 \times 100 = 200\text{ meters}$.

Answer: $200\text{ m}$.

Numerical 1.2

A train moving at $90\text{ km/h}$ applies brakes to produce a uniform deceleration of $-0.5\text{ m/s}^2$. How far will the train go before coming to rest?

Given: $u = 90\text{ km/h} = 90 \times \frac{5}{18} = 25\text{ m/s}$, final velocity $v = 0$, $a = -0.5\text{ m/s}^2$.

Formula: $v^2 = u^2 + 2as \implies 0^2 = (25)^2 + 2(-0.5)s$

Calculation: $0 = 625 - 1s \implies s = 625\text{ m}$.

Answer: Distance covered before rest $= 625\text{ meters}$.

Class 9th Physics • Chapter 2

2. Force, Dynamics & Laws of Motion

Vast Dynamics Theory

2.1 Concept of Force & Inertia

Force is an external push or pull acting on a body that changes or tends to change its state of rest, uniform motion, direction, or shape.

What is Inertia?

Inertia is the inherent property of a body by virtue of which it resists any change in its state of rest or uniform motion in a straight line. Mass is the quantitative measure of inertia. Higher mass $\implies$ Higher Inertia.

Inertia of Rest Passenger jerks backwards when bus suddenly starts.

Inertia of Motion Passenger leans forward when brakes are applied suddenly.

Inertia of Direction Mud flies off tangentially from a rotating vehicle wheel.

2.2 Newton's Three Laws of Motion

Newton's First Law (Law of Inertia)

"An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force."

Newton's Second Law & Mathematical Derivation ($F = ma$)

"The rate of change of momentum of a body is directly proportional to the applied unbalanced force and takes place in the direction in which the force acts."

Linear Momentum ($p$): Product of mass $m$ and velocity $v$ ($p = mv$). SI unit: $\text{kg}\cdot\text{m/s}$.

Initial momentum $p_1 = mu$, Final momentum $p_2 = mv$. Change in momentum $\Delta p = mv - mu = m(v - u)$.

$$\text{Force } F \propto \frac{\Delta p}{t} \implies F \propto \frac{m(v - u)}{t}$$

Since $\frac{v - u}{t} = a$ (acceleration): $F \propto m \cdot a \implies F = k \cdot m \cdot a$. By defining 1 Newton such that constant $k = 1$:

$$F = m \cdot a \quad \text{[SI Unit: Newton (N) = 1 kg}\cdot\text{m/s}^2\text{]}$$

Newton's Third Law of Motion

"To every action, there is an equal and opposite reaction, and they act on two different bodies simultaneously."

$$\vec{F}_{AB} = -\vec{F}_{BA}$$

Examples: Rocket propulsion, walking on ground, recoil velocity of gun when bullet fired.

2.3 Law of Conservation of Momentum (Complete Proof)

Consider two objects $A$ and $B$ of masses $m_1$ and $m_2$ colliding with initial velocities $u_1, u_2$ and final velocities $v_1, v_2$ after collision time $t$.

Force exerted by $A$ on $B$: $F_{AB} = m_2 \left(\frac{v_2 - u_2}{t}\right)$.

Force exerted by $B$ on $A$: $F_{BA} = m_1 \left(\frac{v_1 - u_1}{t}\right)$.

According to Newton's Third Law ($F_{AB} = -F_{BA}$):

$$m_2 \left(\frac{v_2 - u_2}{t}\right) = -m_1 \left(\frac{v_1 - u_1}{t}\right)$$

Cancelling $t$ and expanding: $m_2 v_2 - m_2 u_2 = -m_1 v_1 + m_1 u_1$. Rearranging initial and final terms:

$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \quad \text{[Total Momentum Conserved]}$$

Solved Numerical Bank

Numerical 2.1 (Gun Recoil)

A bullet of mass $20\text{ g}$ is horizontally fired with velocity $150\text{ m/s}$ from a pistol of mass $2\text{ kg}$. What is the recoil velocity of pistol?

Given: $m_1 = 0.02\text{ kg}$, $v_1 = 150\text{ m/s}$, $m_2 = 2\text{ kg}$, initial momentum $= 0$.

Formula: Total final momentum $= 0 \implies m_1 v_1 + m_2 v_2 = 0 \implies v_2 = -\frac{m_1 v_1}{m_2}$.

Calculation: $v_2 = -\frac{0.02 \times 150}{2} = -\frac{3}{2} = -1.5\text{ m/s}$.

Answer: Recoil velocity $= -1.5\text{ m/s}$ (opposite direction).

Class 9th Physics • Chapter 3

3. Universal Gravitation & Floatation Hydrostatics

Vast Astrophysics & Fluids

3.1 Universal Law of Gravitation

Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

$$F = G \frac{m_1 m_2}{r^2}$$

Where Universal Gravitational Constant $G = 6.673 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2$ (measured by Henry Cavendish).

3.2 Acceleration Due to Gravity ($g$) & Mass vs Weight

Derivation of $g$: Consider a body of mass $m$ on Earth's surface of mass $M$ and radius $R$.

Gravitational Force $F = \frac{G M m}{R^2}$. By Newton's Second Law, $F = mg$. Equating both:

$$m g = \frac{G M m}{R^2} \implies g = \frac{G M}{R^2} = 9.8\text{ m/s}^2 \quad \text{(On Earth's surface)}$$

Mathematical Proof: Weight of Object on Moon

Mass of Moon $M_m = \frac{1}{100} M_e$, Radius of Moon $R_m = \frac{1}{4} R_e$.

$$W_{\text{moon}} = \frac{G M_m m}{R_m^2} = \frac{G (M_e/100) m}{(R_e/4)^2} = \frac{16}{100} \frac{G M_e m}{R_e^2} \approx \frac{1}{6} W_{\text{earth}}$$

3.3 Thrust, Pressure & Archimedes' Principle

Thrust & Pressure

$\text{Pressure } P = \frac{\text{Thrust (Perpendicular Force)}}{\text{Area} (A)}$. SI unit: Pascal ($\text{Pa} = \text{N/m}^2$). Smaller area $\implies$ Higher pressure (e.g., sharp needle punctures easily).

Archimedes' Principle

"When a body is fully or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of fluid displaced by it."

Solved Numerical Bank

Numerical 3.1

A stone is dropped from top of a $19.6\text{ m}$ high tower. Calculate its final velocity just before touching ground ($g = 9.8\text{ m/s}^2$).

Given: $u = 0$, $s = 19.6\text{ m}$, $g = +9.8\text{ m/s}^2$.

Formula: $v^2 = u^2 + 2gs = 0 + 2(9.8)(19.6) = (19.6)^2$.

Answer: $v = 19.6\text{ m/s}$.

Class 9th Physics • Chapter 4

4. Work, Kinetic/Potential Energy & Power

Vast Thermodynamics & Work Mechanics

4.1 Scientific Concept of Work

Work is said to be done by a force acting on an object when there is a displacement in the direction of force. $$\text{Work } W = F \cdot s \cdot \cos\theta$$ SI Unit of Work is Joule ($\text{J}$): $1\text{ Joule} = 1\text{ Newton} \times 1\text{ meter}$.

4.2 Kinetic Energy Derivation ($E_k = \frac{1}{2}mv^2$)

Consider an object of mass $m$ initially at rest ($u=0$). A force $F$ accelerates it uniformly to velocity $v$ over displacement $s$.

Work done $W = F \cdot s = (ma) \cdot s$. From third equation $v^2 = u^2 + 2as \implies s = \frac{v^2}{2a}$ (since $u=0$).

$$W = (m a) \times \left(\frac{v^2}{2a}\right) = \frac{1}{2} m v^2$$

$$E_k = \frac{1}{2} m v^2 \quad \text{[Derived]}$$

4.3 Proof of Conservation of Energy (Free Fall Body)

Total Mechanical Energy $E = E_k + E_p$ remains constant at all points during free fall of mass $m$ from height $h$:

At Top Point A ($height = h, v=0$): $E_k = 0, E_p = mgh \implies E_{\text{total}} = mgh$.
At Mid Point B ($fallen\ distance\ x$): $v^2 = 2gx \implies E_k = \frac{1}{2}m(2gx) = mgx$. $E_p = mg(h-x)$. Total $= mgx + mgh - mgx = mgh$.
At Ground Point C ($height = 0$): $v^2 = 2gh \implies E_k = mgh, E_p = 0 \implies E_{\text{total}} = mgh$.

4.4 Power & Commercial Energy Unit

Power is the rate of doing work: $P = \frac{W}{t}$. SI Unit: Watt ($\text{W} = \text{J/s}$).

Commercial Energy Conversion Proof:

$$1\text{ kWh} = 1000\text{ W} \times 3600\text{ s} = 3.6 \times 10^6\text{ Joules}$$

Class 9th Physics • Chapter 5

5. Sound Wave Mechanics, Echo & Ear Structure

Vast Acoustics & Human Physiology

5.1 Production & Propagation of Longitudinal Sound Waves

Sound is a form of mechanical energy that propagates as longitudinal pressure waves consisting of alternating Compressions ($C$) (high density/pressure) and Rarefactions ($R$) (low density/pressure) requiring a material medium.

Fundamental Wave Equation:

$$v = f \cdot \lambda \quad \text{or} \quad v = \frac{\lambda}{T}$$

Where $v$ = Speed of wave, $f$ = Frequency ($\text{Hz}$), $\lambda$ = Wavelength ($\text{m}$), $T$ = Time Period ($\text{s}$).

5.2 Reflection, Echo & Minimum Distance Calculation

An Echo is the repetition of sound caused by reflection from a hard surface. The persistence of hearing in the human brain lasts for approximately $0.1\text{ seconds}$.

Mathematical Calculation for Minimum Distance of Echo:

Speed of sound in air at $22^\circ\text{C} = 344\text{ m/s}$. Time threshold $t = 0.1\text{ s}$.

Total distance travelled by sound to obstacle and back $2d = v \times t = 344 \times 0.1 = 34.4\text{ m}$.

$$d = \frac{34.4}{2} = 17.2\text{ meters} \quad \text{[Minimum distance for distinct echo]}$$

5.3 Applications of Ultrasound & SONAR

Ultrasound refers to sound frequencies above $20,000\text{ Hz} (20\text{ kHz})$.

SONAR (Sound Navigation and Ranging)

Used to measure underwater depth of seas or detect submerged submarines. Transmitter emits ultrasonic pulses; receiver detects reflected echo.

$$2 d = v \cdot t \implies d = \frac{v \cdot t}{2}$$

5.4 Detailed Structure & Functioning of Human Ear

1. Outer Ear

Consists of Pinna which collects sound waves and directs them through the Auditory Canal toward the eardrum.

2. Middle Ear

Contains the Tympanic Membrane (Eardrum) and 3 tiny ossicles bones: Hammer (Malleus), Anvil (Incus), Stirrup (Stapes) which amplify vibrations 20x.

3. Inner Ear

Contains fluid-filled spiral Cochlea. Hair cells convert mechanical pressure waves into electrical nerve impulses sent to brain via Auditory Nerve.

INTERACTIVE PHYSICS LABORATORY

Class 9th Physics Simulators & Solvers

Interactive Kinematics Equation Solver

Input values to instantly compute final velocity ($v$) and displacement ($s$).

u (m/s)

a (m/s²)

t (s)

Final Velocity ($v$): 49.00 m/s

Displacement ($s$): 122.50 m

Universal Planet Weight Calculator

Calculate how heavy an object feels on other celestial bodies ($W = m \cdot g$).

Mass on Earth (kg)

Select Planet/Moon

Weight on Body: 97.20 N

Equivalent Mass Feel: 9.92 kg

TEST YOUR UNDERSTANDING

Class 9th Physics Practice Quiz

QUESTION 1 • MOTION

What is the displacement of an athlete completing 2.5 rounds of a circular track of radius $r$?

QUESTION 2 • GRAVITATION

If the distance between two masses is doubled, the gravitational force between them becomes:

PHYSICS (भौतिक शास्त्र)

Select Physics Chapter

1. Motion in One Dimension & Kinematics

1.1 Fundamental Concepts: Rest & Motion

Scalar Quantities

Vector Quantities

1.2 Distance vs Displacement (Deep Comparative Analysis)

1.3 Derivations of Equations of Motion (Graphical & Algebraic)

1. First Equation of Motion ($v = u + at$)

2. Second Equation of Motion ($s = ut + \frac{1}{2}at^2$)

3. Third Equation of Motion ($v^2 = u^2 + 2as$)

1.4 Uniform Circular Motion

Solved Numerical Problem Bank

2. Force, Dynamics & Laws of Motion

2.1 Concept of Force & Inertia

What is Inertia?

2.2 Newton's Three Laws of Motion

Newton's First Law (Law of Inertia)

Newton's Second Law & Mathematical Derivation ($F = ma$)

Newton's Third Law of Motion

2.3 Law of Conservation of Momentum (Complete Proof)

Solved Numerical Bank

3. Universal Gravitation & Floatation Hydrostatics

3.1 Universal Law of Gravitation

3.2 Acceleration Due to Gravity ($g$) & Mass vs Weight

Mathematical Proof: Weight of Object on Moon

3.3 Thrust, Pressure & Archimedes' Principle

Thrust & Pressure

Archimedes' Principle

Solved Numerical Bank

4. Work, Kinetic/Potential Energy & Power

4.1 Scientific Concept of Work

4.2 Kinetic Energy Derivation ($E_k = \frac{1}{2}mv^2$)

4.3 Proof of Conservation of Energy (Free Fall Body)

4.4 Power & Commercial Energy Unit

5. Sound Wave Mechanics, Echo & Ear Structure

5.1 Production & Propagation of Longitudinal Sound Waves

5.2 Reflection, Echo & Minimum Distance Calculation

Mathematical Calculation for Minimum Distance of Echo:

5.3 Applications of Ultrasound & SONAR

SONAR (Sound Navigation and Ranging)

5.4 Detailed Structure & Functioning of Human Ear

1. Outer Ear

2. Middle Ear

3. Inner Ear

Class 9th Physics Simulators & Solvers

Interactive Kinematics Equation Solver

Universal Planet Weight Calculator

Class 9th Physics Practice Quiz