Topic 9: General Science for Competitive Exams

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Newton’s Three Laws of Motion:

Law	Statement	Everyday Example
First Law (Inertia)	Object at rest stays at rest; object in motion stays in motion unless acted upon by an external force	Passenger lurching forward when a car suddenly brakes
Second Law (F=ma)	Force = Mass × Acceleration	Pushing a loaded cart requires more force than an empty one
Third Law (Action-Reaction)	Every action has an equal and opposite reaction	A rocket pushes gases downward; gases push the rocket upward

Key Formulas:

• Velocity: v = u + at
• Distance: s = ut + ½at²
• Force: F = ma
• Kinetic Energy: KE = ½mv²
• Potential Energy: PE = mgh
• Work: W = F × d × cos(θ)
• Power: P = W/t

Notable Scientists for NABE:

• Isaac Newton — Laws of Motion, Gravitation
• Albert Einstein — E = mc², Theory of Relativity
• Archimedes — Buoyancy, Lever principle
• Michael Faraday — Electromagnetic induction
• Marie Curie — Radioactivity; first woman to win a Nobel Prize

⚡ Exam tip: NABE frequently tests Newton’s laws (especially the second law F=ma), kinetic energy formula, and the difference between speed and velocity. Know the units of key quantities (newton for force, joule for energy, watt for power).

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Motion and Kinematics

Basic Concepts

Distance vs. Displacement:

• Distance: Total path length traveled (scalar — no direction)
• Displacement: Shortest path between two points (vector — has direction)

Speed vs. Velocity:

• Speed: Rate of change of distance (scalar)
• Velocity: Rate of change of displacement (vector — includes direction)

Acceleration: Rate of change of velocity with time

• Formula: a = (v - u) / t
• Unit: meters per second squared (m/s²)
• Positive acceleration: Speed increasing; Negative acceleration (deceleration): Speed decreasing

Equations of Motion (Uniform Acceleration)

These four equations are essential for solving motion problems in NABE:

1. v = u + at (Final velocity = Initial velocity + acceleration × time)
2. s = ut + ½at² (Distance = Initial velocity × time + ½ × acceleration × time²)
3. v² = u² + 2as (Final velocity squared = Initial velocity squared + 2 × acceleration × distance)
4. s = ½(u + v)t (Average velocity × time)

Where:

• u = initial velocity
• v = final velocity
• a = acceleration
• t = time
• s = displacement

Worked Example: A car accelerates from rest (u=0) at 4 m/s² for 5 seconds. Find the distance traveled.

• Using: s = ut + ½at² = 0 + ½ × 4 × 25 = 50 meters

Newton’s Laws of Motion

First Law of Motion — Law of Inertia

An object remains at rest or continues moving in a straight line at constant speed unless an external force acts on it.

Examples:

• Passenger in a car lurching forward when brakes are applied suddenly
• Dust coming off a carpet when it is beaten with a stick
• A book sliding off a table when the tablecloth is pulled quickly

Inertia is the property of an object that resists changes in its state of motion. Mass is a measure of inertia — more mass means more inertia.

Second Law of Motion — F = ma

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Formula: F = ma

Where:

• F = Force (measured in Newtons, N)
• m = Mass (measured in kilograms, kg)
• a = Acceleration (measured in meters per second squared, m/s²)

1 Newton is the force required to accelerate a mass of 1 kg by 1 m/s².

Worked Example: A boy pushes a trolley of mass 20 kg with a force of 50 N. What is the acceleration?

• F = ma → 50 = 20 × a → a = 2.5 m/s²

Third Law of Motion — Action and Reaction

For every action, there is an equal and opposite reaction.

Examples:

• A swimmer pushing water backward (action) moves forward (reaction)
• A rocket expelling hot gases downward (action) is pushed upward (reaction)
• A bullet being fired from a gun (gun kicks back — recoil)

Gravitation

Newton’s Law of Universal Gravitation

Every object in the universe attracts every other object with a force that is:

• Directly proportional to the product of their masses
• Inversely proportional to the square of the distance between them

Formula:

F = G × (m₁ × m₂) / r²

Where:

• F = Gravitational force (N)
• G = Gravitational constant = 6.674 × 10⁻¹¹ Nm²/kg²
• m₁, m₂ = Masses of two objects (kg)
• r = Distance between centers of the two masses (m)

Weight vs. Mass:

• Mass: Amount of matter in an object; constant everywhere (measured in kg)
• Weight: Force of gravity on an object = mg (measured in Newtons)
• g (acceleration due to gravity) on Earth: ~9.8 m/s² (often rounded to 10 m/s² for calculations)
• Weight on the Moon: ~1/6th of weight on Earth (Moon’s gravity is ~1.6 m/s²)

Energy and Work

Forms of Energy

1. Kinetic Energy (KE): Energy of motion

   • Formula: KE = ½mv² (where m = mass in kg, v = velocity in m/s)
   • Unit: Joules (J)

2. Potential Energy (PE): Energy stored due to position or configuration

   • Gravitational PE: PE = mgh (where h = height above ground)
   • Elastic PE: Energy stored in a stretched/compressed spring

3. Mechanical Energy: Sum of KE + PE

4. Other forms: Thermal (heat), Light, Sound, Chemical, Electrical, Nuclear

Work

Work is done when a force causes displacement in the direction of the force.

Formula: W = F × d × cos(θ)

Where:

• W = Work (Joules)
• F = Force (Newtons)
• d = Displacement (meters)
• θ = Angle between force and displacement direction

Special cases:

• If force and displacement are in the same direction (θ = 0°, cos 0 = 1): W = F × d
• If force and displacement are perpendicular (θ = 90°, cos 90 = 0): W = 0 (no work done)

Worked Example: A man lifts a 5 kg bag to a height of 2 m. How much work is done?

• Work = Force × distance = mg × h = 5 × 9.8 × 2 = 98 Joules

Conservation of Energy

Energy cannot be created or destroyed — only transformed from one form to another.

Example: A falling object converts potential energy into kinetic energy:

• At height: Maximum PE, zero KE
• During fall: PE decreases, KE increases
• At ground: Maximum KE, zero PE
• Total mechanical energy remains constant (ignoring air resistance)

Power

Power is the rate of doing work — how quickly work is performed.

Formula: P = W / t

Where:

• P = Power (measured in Watts, W)
• W = Work (Joules)
• t = Time (seconds)

1 Watt = 1 Joule per second

Example: A motor lifts a 100 kg load 10 m in 20 seconds. What is the power?

• Work = mgh = 100 × 9.8 × 10 = 9,800 J
• Power = 9,800 / 20 = 490 Watts

Notable Scientists and Their Discoveries

Scientist	Discovery/Contribution	Year
Isaac Newton	Laws of Motion, Universal Gravitation	1687
Albert Einstein	Theory of Relativity (E = mc²)	1905 (Special), 1915 (General)
Archimedes	Buoyancy principle; Lever principle	~250 BCE
Galileo Galilei	Heliocentric model; Laws of pendulums	1600s
Michael Faraday	Electromagnetic induction; Faraday’s laws	1831
James Clerk Maxwell	Theory of electromagnetism (Maxwell’s equations)	1865
Marie Curie	Discovery of polonium and radium; radioactivity	1898
Niels Bohr	Atomic model (Bohr model of the atom)	1913
Dr. Abdus Salam	Pakistan — Unified Field Theory (we electroweak)	1979 Nobel Prize
A.P.J. Abdul Kalam	India’s missile (Agni, Prithvi) programme	1990s

Albert Einstein — Key Concepts

Special Theory of Relativity (1905):

• The speed of light in a vacuum (c) is the maximum possible speed in the universe: c = 3 × 10⁸ m/s
• Mass-energy equivalence: E = mc² (energy equals mass times the speed of light squared)
• Time dilation: Time passes more slowly for objects moving at high speeds

General Theory of Relativity (1915):

• Gravity is not a force — it is the curvature of spacetime caused by mass and energy
• Heavy objects like stars and black holes curve the space around them

Archimedes — Buoyancy Principle

Archimedes’ Principle: A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

Formula: Buoyant force = Weight of displaced fluid = ρ × V × g

• Where: ρ = density of fluid; V = volume of displaced fluid

Applications:

• Ships float because the weight of water displaced equals the ship’s weight
• Submarines control buoyancy to surface and dive
• Hot air balloons rise because heated air is less dense than surrounding air

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Force and Free Body Diagrams

Types of Forces

Gravitational Force (Weight): Fg = mg (acts downward toward the center of the Earth)

Normal Force: The perpendicular contact force exerted by a surface on an object; acts perpendicular (normal) to the surface

Friction Force: Opposes the relative motion of two surfaces in contact

• Static friction: Prevents motion from starting (f_s ≤ μ_s × N)
• Kinetic friction: Opposes motion already in progress (f_k = μ_k × N)
• μ = coefficient of friction (dimensionless)

Tension Force: The force transmitted through a string, rope, or cable

Applied Force: An external force applied to an object

Free Body Diagram (FBD)

A Free Body Diagram shows all the forces acting on a single object, drawn as arrows from a central point:

Example — Book resting on a table:

        ↑ Normal Force (N)
        |
   [  Book  ]
        |
        ↓ Weight (mg = W)

• Weight (mg) acts downward
• Normal force (N) acts upward (from the table)
• Since the book is at rest, N = mg

Circular Motion

An object moving in a circle has:

• Centripetal acceleration: a_c = v² / r (directed toward the center)
• Centripetal force: F_c = m × v² / r

Key concept: Centripetal force is NOT a new type of force — it is any force (gravity, tension, friction, normal force) that keeps an object moving in a circle.

Example: The Moon orbiting the Earth — gravitational force provides the centripetal force.

Wave Motion and Sound

Wave: A disturbance that transfers energy from one point to another without transferring matter.

Types of Waves:

• Mechanical waves: Require a medium to travel (sound waves, water waves)
• Electromagnetic waves: Do NOT require a medium (light, radio waves, X-rays) — can travel through vacuum

Key Wave Properties:

• Wavelength (λ): Distance between two consecutive crests or troughs (meters)
• Frequency (f): Number of waves per second (Hertz, Hz)
• Wave speed (v): v = f × λ

Sound:

• Speed of sound in air: ~343 m/s at room temperature
• Sound cannot travel through vacuum (needs a medium)
• Infrasound: f < 20 Hz (below human hearing)
• Ultrasound: f > 20,000 Hz (above human hearing; used in medical imaging)

Light and Optics

Speed of light: c = 3 × 10⁸ m/s (in vacuum — fastest speed in the universe)

Reflection: Light bounces off a mirror at the same angle it hits

• Law of reflection: Angle of incidence = Angle of reflection

Refraction: Light bends when passing from one medium to another (e.g., from air to water)

• Example: A pencil appearing bent when placed in water

Lenses:

• Convex (converging) lens: Thicker in middle; used to treat farsightedness (hyperopia)
• Concave (diverging) lens: Thinner in middle; used to treat nearsightedness (myopia)

Electricity and Magnetism

Electric Charge:

• Positive charge: Proton
• Negative charge: Electron
• Unit: Coulomb (C)

Electric Current: Flow of electric charge

• I = Q / t (Current = Charge / Time)
• Unit: Ampere (A)

Voltage (Potential Difference):

• The “pressure” that pushes electric charges through a circuit
• Unit: Volt (V)

Ohm’s Law: V = I × R

• Where: V = Voltage, I = Current, R = Resistance
• Unit of Resistance: Ohm (Ω)

Electric Power: P = V × I = I²R = V² / R

• Unit: Watt (W)

Dr. Abdus Salam — Pakistan’s Nobel Laureate

Dr. Abdus Salam (1926–1996) was a Pakistani theoretical physicist who won the Nobel Prize in Physics in 1979, shared with Sheldon Glashow and Steven Weinberg.

His contribution: The Electroweak Unification — a fundamental theory that unified the electromagnetic force and the weak nuclear force into a single “electroweak” force. This is part of the Standard Model of particle physics.

Historic significance:

• First Pakistani and first Muslim to win a Nobel Prize in science
• He was also a devout Muslim who saw no conflict between science and religion
• Established the International Centre for Theoretical Physics (ICTP) in Trieste, Italy (1964) — a hub for physicists from developing countries

Key Formulas Summary for NABE

Concept	Formula
Velocity (uniform acceleration)	v = u + at
Distance (uniform acceleration)	s = ut + ½at²
Force (Newton’s Second Law)	F = ma
Kinetic Energy	KE = ½mv²
Gravitational Potential Energy	PE = mgh
Work	W = Fd cos(θ)
Power	P = W/t
Weight	W = mg
Wave speed	v = fλ
Ohm’s Law	V = IR
Electric Power	P = VI

⚡ Exam Pattern Insight: NABE’s science section is typically basic. Focus on F = ma, KE = ½mv², v = u + at, and Ohm’s Law. Always include units when answering numerical questions — not giving units is the most common reason for losing marks. Dr. Abdus Salam is the most Pakistan-specific scientist likely to appear on the exam.