Class 9 Physics Notes - AKUEB

Force is a physical quantity that causes an object to change its state of rest or motion. It can make a stationary object move, stop a moving object, change the direction of motion, or alter the shape of an object. Force is a vector quantity, meaning it has both magnitude and direction. The standard international (SI) unit of force is the newton (N). One newton is defined as the force required to accelerate a 1 kg mass by 1 m/s². Mathematically, force is represented as F = ma, where m is mass and a is acceleration.

• Gravitational Force: It is the force of attraction between any two objects with mass. For example, Earth pulls objects toward its center.
• Drag Force: It is the resistive force exerted by a fluid (like air or water) on an object moving through it. It opposes the motion of the object.
• Force of Friction: This force resists the relative motion between two surfaces in contact. It acts opposite to the direction of motion.
• Electrostatic Force: It is the force between two electrically charged objects. Like charges repel, and opposite charges attract each other.
• Magnetic Force: This is the force exerted by magnets or magnetic fields on magnetic materials or moving electric charges.

Different kinds of forces play a vital role in our everyday lives.

For example, gravitational force keeps us grounded on Earth and causes fruits to fall from trees.

Frictional force allows us to walk without slipping, as it provides grip between our shoes and the ground.

Drag force acts on vehicles like cars and airplanes, resisting their motion through air.

Electrostatic forces can be experienced when you rub a balloon on your hair and it sticks to a wall.

Magnetic force is used in everyday tools like refrigerator magnets and electric motors.

These examples show how various forces impact motion, balance, and function in our lives.

Momentum is the quantity of motion an object possesses and is defined as the product of an object's mass and its velocity.

It is a vector quantity, meaning it has both magnitude and direction.

Mathematically, momentum (p) is given by:

p = m × v

Where m is the mass of the object and v is its velocity.

The S.I. unit of momentum is kilogram meter per second (kg·m/s).

Momentum plays a vital role in understanding collisions and motion in physics.

To solve word problems related to force and momentum, we use the relation from Newton’s Second Law:

F = (mv - mu) / t

Where:
F = Force (N)
m = Mass (kg)
u = Initial velocity (m/s)
v = Final velocity (m/s)
t = Time (s)

Example:
A ball of mass 2 kg is moving with an initial velocity of 3 m/s. It is hit and reaches a velocity of 9 m/s in 2 seconds. What is the force applied?

Solution:
Initial momentum = 2 × 3 = 6 kg·m/s
Final momentum = 2 × 9 = 18 kg·m/s
Change in momentum = 18 - 6 = 12 kg·m/s
Time = 2 s
Force = 12 / 2 = 6 N

So, the applied force is 6 newtons.

Law of Conservation of Momentum:

The law states that:
"In a closed system, where no external forces are acting, the total momentum before a collision is equal to the total momentum after the collision."

Mathematically:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where:
m₁ and m₂ = masses of the two bodies
u₁ and u₂ = initial velocities
v₁ and v₂ = final velocities

This principle is widely used in analyzing collisions and explosions in physics.

Difference between Elastic and Inelastic Collisions:

• Elastic Collision: A type of collision in which both momentum and kinetic energy are conserved. Example: Collision between gas molecules.
• Inelastic Collision: A type of collision in which momentum is conserved but kinetic energy is not. Example: A car crash where the vehicles stick together.
• In elastic collisions, objects rebound after impact; in inelastic collisions, they may stick or deform.
• Elastic collisions are ideal and occur mostly at atomic/molecular levels.
• Inelastic collisions are more common in everyday life like sports or vehicle accidents.

Application of the Principle of Conservation of Momentum in Elastic Collision of Two Objects:

In an elastic collision, both momentum and kinetic energy are conserved. Suppose two objects with masses m₁ and m₂ collide elastically. Let their initial velocities be u₁ and u₂, and their final velocities be v₁ and v₂ respectively.

Using conservation of momentum:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Using conservation of kinetic energy:
½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂²

These equations can be solved to find unknown velocities after collision. This principle is used in physics to predict motion after collisions in systems like billiard balls, particles, or even vehicles in controlled environments.

Determining the Velocity After Collision of Two Objects Using the Law of Conservation of Momentum:

The law of conservation of momentum states that the total momentum before collision is equal to the total momentum after collision.

Let two objects of masses m₁ and m₂ have initial velocities u₁ and u₂, and final velocities v₁ and v₂ respectively.

Using the formula:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

✔️ If the masses are equal:
For elastic collision, the objects simply exchange their velocities:
v₁ = u₂, v₂ = u₁

✔️ If the masses are different:
Final velocities can be calculated using these formulas:
v₁ = (m₁ - m₂)u₁ + 2m₂u₂ / (m₁ + m₂)
v₂ = (m₂ - m₁)u₂ + 2m₁u₁ / (m₁ + m₂)

These formulas help us determine how two objects move after colliding, and are commonly used in physics problems involving carts, vehicles, or particles.

Explanation of Vehicle Safety Features Using the Concept of Momentum:

Seat belts, airbags, and crumple zones are crucial safety features in vehicles that help protect passengers during collisions by managing momentum and force.

🔹 Seat Belts: These hold passengers in place and increase the time over which momentum changes during a crash. This reduces the force experienced by the body.

🔹 Airbags: Airbags provide a soft cushion that increases the time of impact, allowing momentum to change more gradually, which reduces injury-causing force.

🔹 Crumple Zones: These are designed areas in a vehicle that deform during a crash. By doing so, they absorb kinetic energy and increase the collision time, decreasing the force transmitted to passengers.

All these features work on the principle that a longer time to change momentum results in a smaller force, thus enhancing passenger safety.

Balanced and Unbalanced Forces:

Balanced Forces: When two or more forces acting on an object are equal in magnitude but opposite in direction, they cancel each other out and do not cause a change in the object's motion. The object remains at rest or continues to move with constant velocity. Example: A book resting on a table experiences balanced forces — gravity pulls it down while the table pushes it up with equal force.

Unbalanced Forces: When the forces acting on an object are not equal and opposite, they result in a net force that causes the object to accelerate or change its motion. Example: If you push a toy car and no other force opposes it, the car moves because the applied force is unbalanced.

Balanced forces maintain the state of motion, while unbalanced forces cause a change in motion.

Difference Between Mass and Weight:

Mass: Mass is the amount of matter in a body. It is a scalar quantity and remains constant everywhere in the universe. The S.I. unit of mass is kilogram (kg).

Weight: Weight is the force with which gravity pulls an object toward the Earth. It is a vector quantity and depends on the gravitational field strength. The S.I. unit of weight is newton (N).

Formula: Weight (W) = Mass (m) × Gravitational acceleration (g)

Example: An object with a mass of 10 kg has a weight of 98 N on Earth (g = 9.8 m/s²).

Solve Word Problems Related to the Concept of Mass and Weight:

• Formula: Weight (W) = Mass (m) × Gravitational acceleration (g)
  Where:
  - W is weight in newtons (N)
  - m is mass in kilograms (kg)
  - g is acceleration due to gravity (9.8 m/s² on Earth)


• Example 1:
  A person has a mass of 60 kg. What is their weight on Earth?
  W = 60 × 9.8 = 588 N
  So, the weight is 588 newtons.


• Example 2:
  An object weighs 490 N on Earth. What is its mass?
  m = W / g = 490 / 9.8 = 50 kg
  So, the mass is 50 kilograms.

• Friction and Vehicle Motion:
  Friction between the tires and the road surface allows a vehicle to move forward. Without sufficient friction, the tires would spin without gripping the road, preventing proper motion.
• Type of Surface:
  Rough surfaces provide more friction, which helps in better traction and control of the vehicle. Smooth or oily surfaces reduce friction, increasing the risk of slipping or loss of control.
• Road Conditions and Skidding:
  On wet, icy, or muddy roads, friction is greatly reduced, increasing the chances of skidding. Skidding occurs when the tires lose grip, making it hard to steer or stop the vehicle effectively.
• Braking Force:
  When brakes are applied, friction between brake pads and wheels slows down the vehicle. The friction between the tires and road is also critical to stop the car safely without skidding.
• Conclusion:
  Friction plays a vital role in controlling vehicle speed, direction, and stopping. It is influenced by road conditions and tire quality, which is why proper maintenance and careful driving are essential.

• Rolling Friction:
  Rolling friction occurs when an object rolls over a surface. For example, the friction between car tires and the road is rolling friction.
• Sliding Friction:
  Sliding friction occurs when two surfaces slide directly over each other, such as dragging a box across the floor.
• Comparison:
  Rolling friction is much smaller than sliding friction because in rolling, less surface area is in contact and there is less resistance to motion.
• Practical Example:
  A suitcase with wheels (rolling) is easier to move than one without wheels (sliding), because rolling friction is lower.
• Conclusion:
  Rolling friction is preferred in vehicles and machines to reduce energy loss and make movement smoother and more efficient.

• Using Lubricants: Applying oil, grease, or graphite between moving surfaces reduces direct contact and minimizes friction.
• Using Ball Bearings: Ball bearings reduce sliding friction by converting it into rolling friction, which is much lower.
• Polishing Surfaces: Smoother surfaces cause less resistance, hence reducing friction.
• Streamlining: Designing the shape of objects (like vehicles or airplanes) to reduce air resistance, a form of fluid friction.
• Using Rollers or Wheels: Moving objects using rollers or wheels reduces friction compared to dragging or sliding them.
• Using Suitable Materials: Using materials with low coefficients of friction (like Teflon) for contact surfaces helps in reducing friction.

• Centripetal Force: It is the force that keeps a body moving in a circular path and is always directed towards the center of the circle.
• Explanation: When an object moves in a circle, it constantly changes direction. This continuous change requires a force, which acts inward towards the center. This is called centripetal force.
• Example: When a stone is tied to a string and swung in a circle, the tension in the string provides the centripetal force that keeps the stone moving in a circular path.
• S.I. Unit: The S.I. unit of centripetal force is the newton (N).

• When an object moves in a curved or circular path, a force acts on it that is always perpendicular to its velocity.
• This perpendicular force does not change the speed (magnitude) of the object but continuously changes its direction of motion.
• This force is known as the centripetal force, and it always acts towards the center of the curved path.
• Since the direction of velocity changes while speed remains constant, the object is said to be accelerating.
• Example: A car turning on a curved road experiences a force from friction between the tires and the road, which acts toward the center of the curve and keeps the car moving along the curve without changing its speed.

• The centripetal force is the force required to keep an object moving in a circular path.
• It is always directed towards the center of the circle and is responsible for changing the direction of the object's velocity.
• The formula for calculating centripetal force is:

  Fc = (mv²) / r

• Where:
• F_c = Centripetal force (N)
• m = Mass of the object (kg)
• v = Speed of the object (m/s)
• r = Radius of the circular path (m)
• Example: If a 2 kg object is moving with a speed of 4 m/s in a circle of radius 3 m, then:

  Fc = (2 × 4²) / 3 = (2 × 16) / 3 = 32 / 3 ≈ 10.67 N

• Moment of force (also called torque) is the turning effect of a force applied to a rotating object around a pivot point.
• It depends on two factors:
  • The magnitude of the force applied.
  • The perpendicular distance from the pivot to the line of action of the force.
• Formula:

  Moment (Torque) = Force × Perpendicular Distance

• Unit: Newton meter (N·m)
• Example: If a force of 10 N is applied at a perpendicular distance of 0.5 m from a pivot, then:

  Moment = 10 × 0.5 = 5 N·m

• This means the force creates a turning effect (moment) of 5 Newton meters around the pivot point.

• The turning effect of force (or torque) is observed in many everyday activities where a force causes an object to rotate around a fixed point (pivot).
• Examples from daily life include:
• Opening a door: When we push the door far from the hinge (pivot), it opens easily because the perpendicular distance is large, producing more torque.
• Using a spanner/wrench: Applying force at the end of a long wrench helps loosen tight bolts because of the greater moment arm.
• Seesaw on a playground: Two children of different weights can balance by adjusting their distance from the pivot point.
• Pedaling a bicycle: The force applied on the pedal creates torque that rotates the gears and moves the bicycle.
• Turning a steering wheel: Applying force on the outer edge of the wheel turns it more effectively due to a greater torque.
• Conclusion: The greater the force or the longer the perpendicular distance from the pivot, the stronger the turning effect (moment of force).

• The principle of moments states that:
• "If a body is in equilibrium, then the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot."
• Mathematically, it can be written as:
• ∑ Clockwise Moments = ∑ Anticlockwise Moments
• This principle is used to maintain balance in seesaws, weighing scales, and levers in real-life applications.
• It helps us solve problems related to balance and equilibrium in mechanical systems.

• To solve word problems based on the principle of moments, apply the rule:
• Total Clockwise Moment = Total Anticlockwise Moment
• Example: A uniform meter rod is balanced at its midpoint. A 5 N weight is hung at 20 cm from the pivot. Where should a 10 N weight be placed to balance the rod?
• Solution:
• Let the 10 N weight be placed at a distance x cm on the other side of the pivot.
• Clockwise moment = 5 N × 30 cm = 150 N·cm
• Anticlockwise moment = 10 N × x cm
• Equating both moments: 10x = 150 → x = 15 cm
• Answer: The 10 N weight should be placed 15 cm from the pivot on the opposite side.

• The centre of gravity of a body is the point at which the entire weight of the body appears to act.
• In a uniform gravitational field, the centre of gravity and the centre of mass of a body lie at the same point.
• It is the point where the torque due to the weight of the body is zero in all directions when the body is supported at that point.
• For regular-shaped objects, the centre of gravity is usually at the geometric centre (e.g., the centre of a sphere or rectangle).
• The concept of centre of gravity is important for balance, stability, and structural design.

• A couple is a pair of equal and opposite forces acting on a body but not along the same line.
• These forces are parallel but act in opposite directions and at different points, creating a turning effect or rotation.
• A couple does not cause any linear motion but only tends to rotate the object about an axis.
• The moment of a couple is calculated as: Moment = Force × Distance between the forces.
• Examples of couples include turning a steering wheel or opening a bottle cap.

• A couple produces rotation, and the turning effect (moment) created by it is called the moment of the couple.
• Unlike a single force, the moment of a couple is independent of the point about which it is measured.
• This means that the value of the moment remains the same from any point or axis in the plane of the couple.
• This property makes a couple unique and useful in rotational systems where the point of rotation is not fixed.
• Moment of the couple = Force × Perpendicular distance between the forces
• Example: Turning a tap or steering a wheel – the effect remains the same regardless of where it is measured from.

• Equilibrium is a state in which all the forces and moments acting on a body are balanced.
• In equilibrium, the body either remains at rest or continues to move with a constant velocity.
• There are two main types of equilibrium: static equilibrium (body at rest) and dynamic equilibrium (body moving with constant velocity).
• For a body to be in equilibrium:
  • The sum of all forces acting on it must be zero (∑F = 0).
  • The sum of all moments (torques) acting on it must also be zero (∑τ = 0).
• Example: A book lying on a table is in static equilibrium because all forces acting on it are balanced.

• 1. Stable Equilibrium: When a body, after being slightly disturbed, returns to its original position.
  Example: A cone placed on its base comes back to its original position if tilted slightly.
• 2. Unstable Equilibrium: When a body, after being slightly disturbed, moves further away from its original position.
  Example: A cone balanced on its tip falls when slightly disturbed.
• 3. Neutral Equilibrium: When a body, after being slightly disturbed, stays in its new position without returning or moving further away.
  Example: A ball placed on a flat surface stays at its new position when rolled slightly.

• 1. First Condition (Translational Equilibrium): The sum of all the forces acting on a body must be zero.
  Mathematically: ΣF = 0
• 2. Second Condition (Rotational Equilibrium): The sum of all the torques (moments) acting on a body must also be zero.
  Mathematically: Στ = 0

When both conditions are satisfied, the body is said to be in complete equilibrium.

• 1. Translational Equilibrium: This occurs when the sum of all external forces acting on a body is zero. The body remains at rest or moves with constant velocity.
  Example: A book lying on a table experiences gravitational force downward and normal force upward, which cancel each other out.
• 2. Rotational Equilibrium: This occurs when the sum of all torques (moments) acting on a body is zero. The body does not rotate or rotates with constant angular velocity.
  Example: A balanced seesaw where the clockwise and anticlockwise moments are equal.
• 3. Static Equilibrium: When a body is at rest and all forces and torques are balanced.
  Example: A ladder leaning against a wall without slipping.
• 4. Dynamic Equilibrium: When a body is moving with constant velocity and there is no change in motion due to balanced forces.
  Example: A car moving at a constant speed on a straight road.

To solve such problems, apply the Principle of Moments:

Total Clockwise Moments = Total Anticlockwise Moments

Example:
A uniform meter rule is balanced at the 50 cm mark. A 2 kg mass is hung at the 20 cm mark. Where should a 3 kg mass be hung to balance the rule?

Solution:

• Let the pivot be at 50 cm mark.
• Clockwise moment = 2 kg × (50 - 20) = 2 × 30 = 60 kg·cm
• Let the position of 3 kg mass be x cm, so distance from pivot = (x - 50)
• Anticlockwise moment = 3 × (x - 50)

Now apply the condition for balance:

2 × 30 = 3 × (x - 50)

60 = 3(x - 50)

60 = 3x - 150

3x = 210

x = 70

Answer: The 3 kg mass should be hung at the 70 cm mark.

• 1. Stable Equilibrium: A body is in stable equilibrium if, when slightly displaced, it returns to its original position. This happens when the center of gravity rises and then falls back.
  Example: A cone resting on its base. When tilted, it returns to its original position.
• 2. Unstable Equilibrium: A body is in unstable equilibrium if, when slightly displaced, it moves further away from its original position. The center of gravity falls and continues to fall.
  Example: A cone balanced on its tip. Any slight disturbance will topple it over.
• 3. Neutral Equilibrium: A body is in neutral equilibrium if, when displaced, it stays in its new position. The center of gravity neither rises nor falls.
  Example: A ball lying on a flat horizontal surface. It remains at rest wherever it is moved.

The stability of an object depends greatly on the position of its centre of gravity and the size of its base. The following points explain this relationship:

• Lower Centre of Gravity: An object with a low centre of gravity is more stable. It requires a larger force or tilt to make it topple.
  Example: A wide-bottomed vase is more stable than a tall narrow one.
• Higher Centre of Gravity: An object with a high centre of gravity is less stable. It topples easily when slightly tilted.
  Example: A tall, thin tower is less stable and more likely to fall over.
• Wider Base of Support: A wider base increases the stability of an object by allowing the centre of gravity to move further without falling outside the base.
  Example: A triangle-shaped traffic cone is stable because of its wide base and low centre of gravity.
• Vertical Line Through Centre of Gravity: For an object to remain stable, the vertical line drawn from its centre of gravity must fall within its base. If this line falls outside the base, the object will topple.

Conclusion: To improve the stability of an object, lower its centre of gravity and widen its base.

Newton’s Law of Gravitation states that:

• Every object in the universe attracts every other object with a force.
• This gravitational force is directly proportional to the product of their masses.
• It is inversely proportional to the square of the distance between their centres.

Mathematically:

F = G × (m₁ × m₂) / r²

• F = Gravitational force between the two objects
• G = Universal gravitational constant (6.674 × 10⁻¹¹ Nm²/kg²)
• m₁ and m₂ = Masses of the two objects
• r = Distance between the centres of the two masses

According to Newton’s Third Law of Motion, “To every action, there is an equal and opposite reaction.”

This law also applies to gravitational forces:

• If object A attracts object B with a certain gravitational force, then object B also attracts object A with an equal and opposite gravitational force.
• The magnitudes of the gravitational forces between two objects are equal, but the directions are opposite.
• This mutual force of attraction acts along the line joining the centers of the two objects.

Example:

The Earth pulls the Moon with a gravitational force, and the Moon pulls the Earth with an equal but opposite force.

This perfectly demonstrates the consistency of gravitational force with Newton’s Third Law.

A gravitational field is a region of space surrounding a mass where another mass experiences a force of attraction due to gravity.

• It is an example of a field of force, which means that an object can exert a force on another object without physical contact.
• The gravitational field is always attractive and acts towards the mass creating the field.
• Any object placed in the gravitational field of another mass will experience a force pulling it toward that mass.

Field Lines:

• Gravitational field lines are directed towards the mass creating the field.
• The closer the field lines, the stronger the field at that point.

Gravitational Field Strength (g):

The strength of a gravitational field at a point is defined as the force experienced by a unit mass placed at that point.

g = F / m

• F = Force experienced by a mass
• m = Mass of the object
• g = Gravitational field strength (units: N/kg)

Example: Earth has a gravitational field around it, so any object near the Earth experiences a downward force due to gravity.

Weight is the force exerted on a body due to gravity. It is the result of the gravitational attraction between the object and the Earth (or any other celestial body).

Mathematically, weight is given by the formula:

W = m × g

• W = Weight of the object (in Newtons, N)
• m = Mass of the object (in kilograms, kg)
• g = Gravitational field strength (in N/kg), approximately 9.8 N/kg on Earth

Key Points:

• Weight is a vector quantity; it acts vertically downward toward the center of the Earth.
• Unlike mass, weight can change depending on the gravitational field strength of the location (e.g., it is less on the Moon than on Earth).
• Weight is the force that gives an object a sense of heaviness.

Example: An object with a mass of 10 kg on Earth has a weight of:

W = 10 × 9.8 = 98 N

Newton’s Law of Universal Gravitation states that 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 their centers

The formula is:

F = G × (m₁ × m₂) / r²

• F = Gravitational force (in Newtons, N)
• G = Gravitational constant = 6.674 × 10^-11 N·m²/kg²
• m₁ and m₂ = Masses of the two objects (in kilograms)
• r = Distance between the centers of the two objects (in meters)

Example Problem:

Calculate the gravitational force between two objects with masses of 5 kg and 10 kg placed 2 meters apart.

Solution:

Using the formula:

F = G × (m₁ × m₂) / r²

F = (6.674 × 10^-11) × (5 × 10) / (2)²

F = (6.674 × 10^-11) × 50 / 4

F = 8.3425 × 10^-10 N

Answer: The gravitational force between the two objects is approximately 8.34 × 10^-10 N.

Note: Gravitational force is very small between ordinary objects but becomes significant with very large masses such as planets or stars.

We can calculate the mass of the Earth by rearranging Newton's Law of Gravitation and using the known values of:

• The gravitational force on an object (its weight)
• The radius of the Earth
• The gravitational constant (G)

Step-by-step Derivation:

Newton’s law of gravitation is:

F = G × (M × m) / R²

• F = Weight of an object on Earth's surface (N)
• G = Gravitational constant = 6.674 × 10^-11 N·m²/kg²
• M = Mass of Earth (what we want to find)
• m = Mass of the object
• R = Radius of Earth = 6.371 × 10⁶ m

We also know that F = m × g, where g = 9.8 m/s²

Equating the two expressions for force:

m × g = G × (M × m) / R²

Cancel m from both sides:

g = G × M / R²

Rearrange to find M:

M = g × R² / G

Substitute values:

M = (9.8) × (6.371 × 10⁶)² / (6.674 × 10^-11)

M ≈ 5.97 × 10²⁴ kg

Answer: The mass of Earth is approximately 5.97 × 10²⁴ kilograms.

The acceleration due to gravity (g) on the surface of the Earth is approximately 9.8 m/s². However, as we move away from the Earth's surface (i.e., increase altitude), the value of g decreases. This is because gravitational force becomes weaker with distance from the center of the Earth.

Reason:

The formula for gravitational acceleration at a distance r from the center of the Earth is:

g = G × M / r²

• G = Universal gravitational constant
• M = Mass of Earth
• r = Distance from the center of the Earth (i.e., radius of the Earth + altitude)

As altitude increases, the distance r increases, and since r² is in the denominator, the value of g decreases.

Conclusion: The acceleration due to gravity decreases with altitude because gravitational force weakens as the distance from Earth's center increases.

Newton’s law of universal gravitation is fundamental in explaining and predicting the motion of satellites around the Earth and other celestial bodies.

Newton’s Law of Gravitation: Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F = G × (m₁ × m₂) / r²

• F = Gravitational force
• G = Universal gravitational constant
• m₁ and m₂ = Masses of two bodies (e.g., Earth and satellite)
• r = Distance between their centers

Importance in Satellite Motion:

• Gravitational force acts as the centripetal force that keeps satellites in orbit around the Earth.
• It helps calculate the orbital speed and period of a satellite.
• Determines the height of the satellite above the Earth for stable orbits.
• Allows engineers to design satellites for communication, weather forecasting, and GPS using orbital mechanics.

Conclusion: Newton’s law of gravitation is essential to understand and calculate the forces involved in satellite motion, making it a cornerstone in the field of space science and satellite technology.

5.5.1 Explanation: Planets Have Moons and They Orbit Around Them

Moons (also called natural satellites) are celestial bodies that revolve around planets due to the gravitational attraction between the moon and the planet.

• Every planet in our solar system, except Mercury and Venus, has at least one moon.
• Moons stay in orbit around their planets because of the gravitational force exerted by the planet, which acts as the centripetal force needed to keep the moon moving in a curved path.
• This motion is similar to how satellites orbit the Earth or how planets orbit the Sun — it’s governed by Newton’s Law of Universal Gravitation.
• The moon’s inertia (its tendency to move in a straight line) and the planet’s gravity combine to create a stable orbit.

Example:

• Earth has one moon that completes an orbit approximately every 27.3 days.
• Jupiter has more than 90 moons, including the four largest known as the Galilean moons (Io, Europa, Ganymede, and Callisto).

Conclusion: Moons orbit planets due to the gravitational force exerted by the planet. This natural motion follows the same physical laws that govern the movement of all celestial bodies, such as Newton’s law of gravitation and the concept of centripetal force.

1. Moon to Orbit the Earth:
   • The Earth exerts a gravitational force on the Moon.
   • This force pulls the Moon towards the Earth and acts as the centripetal force, keeping the Moon in a curved orbital path instead of moving in a straight line.
   • The Moon's motion is a result of its inertia (tendency to move forward) and the gravitational pull from Earth creating a balance that maintains orbit.
2. Artificial Satellites to Orbit the Earth:
   • Artificial satellites are man-made objects launched into space to revolve around Earth for communication, weather, navigation, and research.
   • Once launched with the right speed and direction, Earth's gravitational force pulls the satellite towards it.
   • The satellite’s forward velocity and Earth's gravity together result in a continuous free fall around Earth, forming a stable orbit — just like the Moon.
   • This gravitational pull acts as a centripetal force required for circular motion.
3. Planets to Orbit the Sun:
   • The Sun, having a massive gravitational pull due to its enormous mass, attracts all the planets towards it.
   • Each planet moves in a curved path (orbit) around the Sun due to the Sun's gravity pulling inward and the planet's inertia moving it forward.
   • This balance creates elliptical orbits, as described by Kepler’s laws of planetary motion.

Conclusion: Gravitational force is the key reason behind the orbital motion of moons, satellites, and planets. It acts as the necessary centripetal force that keeps these celestial objects in stable orbits.

The universe is unimaginably vast and contains everything that exists — including matter, energy, planets, stars, solar systems, galaxies, and space itself.

• Galaxies:
  • A galaxy is a massive system made up of billions of stars, gas, dust, and dark matter, all held together by gravitational force.
  • The universe is home to billions of galaxies, each varying in size, shape, and structure. Examples include spiral galaxies like the Milky Way (our galaxy), elliptical galaxies, and irregular galaxies.
• The Expanding Universe:
  • Scientific observations (especially by Edwin Hubble) show that galaxies are moving away from each other.
  • This movement indicates that the universe is not static but is expanding in all directions.
  • The farther a galaxy is, the faster it appears to be receding — a phenomenon known as Hubble's Law.
  • This discovery led to the widely accepted theory that the universe began with a huge explosion known as the Big Bang, and it has been expanding ever since.
• Conclusion:
  • The universe is a dynamic, ever-expanding collection of galaxies.
  • Understanding this helps us explore the origin, structure, and future of the cosmos.

• Orbit Shape:
  • Planets follow nearly circular orbits around the Sun due to their stable and consistent motion.
  • Comets follow highly elliptical (oval-shaped) orbits which bring them very close to the Sun at one point (perihelion) and very far away at another (aphelion).
• Speed Variation:
  • As a comet approaches the Sun, its speed increases due to the Sun’s strong gravitational pull.
  • When moving away from the Sun, it slows down significantly.
  • Planets also change speed slightly due to their elliptical orbits, but their variation is much less dramatic than that of comets.
• Orbital Time:
  • Planets take predictable and regular times to complete one orbit around the Sun. For example, Earth takes 365.25 days.
  • Comets can take years, decades, or even centuries to complete one orbit, depending on how elongated their orbits are.
• Path and Visibility:
  • Planets are visible throughout the year and follow a path close to the ecliptic plane (same general plane as Earth).
  • Comets can appear from any direction and are only visible when they are close to the Sun and Earth, often developing bright tails due to solar radiation and wind.
• Conclusion:
  • The main difference lies in the shape, orientation, speed variation, and orbital time of their paths around the Sun.
  • While planets maintain regular, stable orbits, comets follow long, stretched, and more unpredictable paths.

• Definition of Work:
  • Work is said to be done when a force is applied on an object and the object moves in the direction of the applied force.
  • Mathematically, Work (W) = Force (F) × Displacement (d) × cos(θ),
  • Where θ is the angle between force and displacement directions.
• Conditions for Work:
  • Work is only done if the object is displaced.
  • No work is done if there is no movement or if force is perpendicular to displacement.
• SI Unit of Work:
  • The SI unit of work is the joule (J).
  • 1 joule is defined as the work done when a force of 1 newton moves an object 1 meter in the direction of the force.
  • 1 J = 1 N × 1 m

• Formula to Use:
  • Work Done (W) = Force (F) × Displacement (d) × cos(θ)
• Example 1:
  • Problem: A person pushes a box with a force of 50 N over a distance of 10 m in the same direction as the force. Find the work done.
  • Solution: W = F × d × cos(0°) = 50 × 10 × 1 = 500 J
• Example 2:
  • Problem: A man pulls a cart with a force of 100 N at an angle of 60° to the horizontal and moves it 5 m. Find the work done.
  • Solution: W = 100 × 5 × cos(60°) = 100 × 5 × 0.5 = 250 J
• Example 3 (Zero Work):
  • Problem: A man carries a bag of 20 N weight while walking horizontally on a flat road for 15 m. What is the work done?
  • Solution: Since the direction of force (vertical) and displacement (horizontal) are perpendicular, cos(90°) = 0 ⇒ W = 0 J

• Energy: Energy is the capacity of a body to do work. It exists in many forms, such as mechanical, thermal, chemical, and nuclear.
• Kinetic Energy (KE): It is the energy possessed by a body due to its motion. Any object in motion has kinetic energy.
• Formula: KE = (1/2)mv²
• Where: m = mass of the body, v = velocity of the body
• Potential Energy (PE): It is the energy possessed by a body due to its position or configuration. It is commonly observed in objects raised to a height.
  • Formula: PE = mgh
  • Where: m = mass, g = acceleration due to gravity, h = height from the ground
• SI Unit of Energy: The SI unit of energy is joule (J).

• Derivation of Kinetic Energy (KE):
• Work done (W) on a body is equal to the change in its kinetic energy.
• Work = Force × Distance
• From Newton’s second law: Force (F) = ma
• If the object starts from rest and covers distance s under constant acceleration a, then:
• Using the equation: v² = u² + 2as (where u = 0)
• ⇒ v² = 2as ⇒ s = v² / 2a
• Now, Work done = F × s = ma × (v² / 2a) = (1/2)mv²
• ∴ Kinetic Energy (KE) = (1/2)mv²
• Derivation of Potential Energy (PE):
• Potential energy is the work done in raising a body to a height h against gravity.
• Work = Force × Distance
• Force required = weight of object = mg
• Distance moved = h
• Work done = mgh
• ∴ Potential Energy (PE) = mgh

• Example 1 – Kinetic Energy:
• Problem: A car of mass 1000 kg is moving with a speed of 20 m/s. Calculate its kinetic energy.
• Solution:
• Given: m = 1000 kg, v = 20 m/s
• Formula: KE = (1/2)mv²
• KE = (1/2) × 1000 × (20)² = 500 × 400 = 200,000 J
• Example 2 – Potential Energy:
• Problem: A body of mass 10 kg is lifted to a height of 5 meters. Calculate its potential energy. (Take g = 9.8 m/s²)
• Solution:
• Given: m = 10 kg, h = 5 m, g = 9.8 m/s²
• Formula: PE = mgh
• PE = 10 × 9.8 × 5 = 490 J
• Example 3 – Conversion between PE and KE:
• Problem: An object of mass 2 kg falls from a height of 10 m. What is its kinetic energy just before hitting the ground?
• Solution:
• Initial PE = mgh = 2 × 9.8 × 10 = 196 J
• Since no energy is lost, all PE is converted into KE at the bottom.
• ∴ KE = 196 J

• Kinetic Energy (KE): The energy possessed by a moving object.
• Example: A moving car, flowing water, or a running person.
• Potential Energy (PE): The energy stored in an object due to its position or configuration.
• Example: Water stored in a dam, a stretched rubber band, or a rock at a height.
• Elastic Potential Energy: Stored in stretched or compressed elastic materials.
• Example: Spring in a toy gun or a compressed spring in a machine.
• Chemical Energy: Stored in the bonds of chemical compounds.
• Example: Batteries, food, or fuels like petrol and gas.
• Gravitational Potential Energy: Stored due to an object’s height in the Earth’s gravitational field.
• Example: A book on a shelf, or a person standing at the top of a slide.
• Thermal Energy: Energy due to the motion of particles in matter, felt as heat.
• Example: Boiling water, hot iron, or the sun.
• Electrical Energy: Carried by moving electrons in a conductor.
• Example: Power in wires, lightning, or electric appliances.
• Nuclear Energy: Stored in the nucleus of an atom, released during nuclear reactions.
• Example: Nuclear power plants or atomic bombs.
• Sound Energy: Produced by vibrating objects and travels in waves.
• Example: Musical instruments, speakers, or human voice.
• Light Energy (Radiant Energy): Carried by light waves.
• Example: Sunlight, laser beams, or a light bulb.

6.4.1 State the Law of Conservation of Energy

• Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only be transformed from one form to another, but the total amount of energy in an isolated system remains constant.
• This means that the total energy before a process is equal to the total energy after the process, although the form of energy may change.
• Mathematically: Total Energy (Initial) = Total Energy (Final)
• Examples:
  • When a ball is thrown upward, kinetic energy is converted into potential energy. As it falls back, potential energy is converted back into kinetic energy.
  • In a pendulum, energy continuously shifts between kinetic and potential forms, but the total energy remains constant.
  • In power plants, chemical or nuclear energy is converted into electrical energy without loss of total energy (though some may be lost as heat or sound).
• This law is one of the fundamental principles of physics and applies universally in all natural processes.

• Energy can be transformed from one form to another through various physical, chemical, or mechanical processes. These conversions are essential for performing useful work in daily life and technology.
• Common Energy Conversions:
  • Chemical to Thermal: In a gas stove, chemical energy in fuel is converted into heat energy.
  • Chemical to Electrical: In batteries, chemical energy is converted into electrical energy to power devices.
  • Electrical to Light: In light bulbs, electrical energy is transformed into light energy (and some heat).
  • Electrical to Mechanical: In electric fans and motors, electrical energy is converted into mechanical energy (motion).
  • Mechanical to Electrical: In a generator, the motion of a turbine is converted into electrical energy.
  • Solar to Electrical: Solar panels convert solar energy directly into electrical energy using photovoltaic cells.
  • Nuclear to Thermal: In nuclear reactors, nuclear energy is converted into heat, which is then used to produce electricity.
• Real-Life Examples:
  • In a hydroelectric power station, water’s potential energy is converted into kinetic energy, which then turns turbines to generate electricity.
  • In a human body, food (chemical energy) is broken down to produce energy for movement (mechanical) and maintaining body temperature (thermal).
• These energy conversions are governed by the law of conservation of energy, which ensures no energy is lost, only changed in form.

• 1. Mass Can Be Converted into Energy: The equation E = mc² shows that mass is a form of energy. A small amount of mass can be converted into a large amount of energy because the speed of light squared (c²) is a very large number.
• 2. Energy and Mass Are Interchangeable: Mass and energy are two sides of the same coin. This principle means that energy can also be converted into mass under the right conditions, such as in particle physics experiments.
• 3. Applications in Nuclear Reactions: This equation explains how nuclear reactions (like fission and fusion) release enormous energy by converting a small part of mass into energy. It is the principle behind nuclear power and atomic bombs.

Electricity generation using fossil fuels involves multiple energy conversions. Below is a simple block diagram illustrating the process:

• Fossil Fuels (Coal, Oil, Gas) →
• Boiler (burns fuel to heat water into steam) →
• Steam →
• Turbine (steam rotates turbine blades) →
• Generator (turbine spins generator to produce electricity) →
• Transformer (steps up voltage for transmission) →
• Transmission Lines →
• Electricity Output to Homes and Industry

Energy Conversions Involved:

• Chemical Energy (from fuel) → Heat Energy (in boiler)
• Heat Energy → Kinetic Energy (steam turning turbine)
• Kinetic Energy → Electrical Energy (generator)

• Air Pollution: Burning fossil fuels like coal, oil, and gas releases harmful gases such as carbon dioxide (CO₂), sulfur dioxide (SO₂), and nitrogen oxides (NO_x), contributing to global warming, acid rain, and respiratory problems.
• Greenhouse Gas Emissions: Power plants, especially those using fossil fuels, emit large amounts of CO₂, a major greenhouse gas responsible for climate change.
• Water Pollution: Thermal power plants use large amounts of water for cooling. Heated discharge water and accidental chemical leaks can harm aquatic ecosystems.
• Land Degradation: Mining for coal and drilling for oil damages land, forests, and habitats. It also causes soil erosion and affects biodiversity.
• Radioactive Waste: Nuclear power generation produces radioactive waste, which requires safe and long-term disposal due to its harmful effects on human health and the environment.
• Thermal Pollution: Discharge of hot water into rivers or lakes from power stations raises water temperatures, affecting aquatic life.
• Noise Pollution: Power plants and their associated machinery (turbines, generators) create noise that can disturb nearby communities.
• Resource Depletion: Fossil fuels are non-renewable resources, and excessive usage leads to their depletion, leaving fewer resources for future generations.

• Non-renewable energy sources: These are energy sources that cannot be replaced once they are used. They are finite and will eventually run out. Examples include coal, oil, natural gas, and nuclear fuel.
• Renewable energy sources: These are energy sources that are naturally replenished and do not run out. Examples include sunlight (solar energy), wind, water (hydropower), biomass, and geothermal energy.

Non-renewable energy sources have been widely used for decades and are still the major contributors to global energy production. However, their use leads to several environmental problems such as greenhouse gas emissions, air pollution, and global warming. Since these resources are limited, they are becoming more expensive and difficult to extract with time. On the other hand, renewable energy sources are considered cleaner and more sustainable alternatives. Solar panels convert sunlight directly into electricity, wind turbines harness the power of moving air, and hydropower plants use flowing water to generate electricity. These sources produce little to no harmful emissions and help reduce our dependency on fossil fuels. Governments and environmental organizations around the world are encouraging the adoption of renewable energy to ensure a cleaner and safer future. Investing in renewable energy helps in conserving natural resources, reducing pollution, and promoting sustainable development.

• Electric Motor: Converts electrical energy into mechanical energy. When electric current passes through the motor's coil, it generates a magnetic field that interacts with permanent magnets inside the motor. This interaction causes the coil to rotate, producing mechanical motion used to drive machines and appliances.
• Electric Generator: Converts mechanical energy into electrical energy. It operates on the principle of electromagnetic induction, where a moving coil or magnet inside the generator induces an electric current in the wire. This current is then transmitted for domestic or industrial use.
• Hydroelectric Power Station: Converts the potential and kinetic energy of stored or flowing water into electrical energy. Water from a reservoir flows through turbines, causing them to spin. These spinning turbines are connected to generators which convert the mechanical energy into electricity.
• Thermal Power Station: Converts chemical energy of fuels like coal or gas into thermal energy, which is then used to produce steam. The steam rotates turbines, which are connected to generators, converting thermal energy into mechanical and then electrical energy.
• Solar Panel: Converts solar energy (sunlight) directly into electrical energy using photovoltaic cells. These cells contain semiconductors like silicon, which release electrons when exposed to sunlight, generating electricity.
• Wind Turbine: Converts kinetic energy of moving air into mechanical energy, which is then converted into electrical energy by a generator connected to the rotating blades.

In each of these systems, the basic principle involves transforming one form of energy into another to perform useful work or generate electricity. The efficiency and environmental impact of each method can vary, making renewable energy conversion methods more favorable in today’s world.

Efficiency of a working system refers to the ratio of useful output energy (or work) to the total input energy (or work), usually expressed as a percentage. It indicates how effectively a machine or system converts input energy into useful output.

• Formula: Efficiency (%) = (Useful Output Energy / Input Energy) × 100
• An efficient system wastes less energy, often in the form of heat, sound, or friction.
• No real system is 100% efficient due to unavoidable energy losses.

To calculate the efficiency of any energy conversion process, we use the following formula:

• Efficiency (%) = (Energy Converted into the Required Form / Total Energy Input) × 100

This formula helps in determining how much of the input energy is successfully transformed into the desired useful output. For example, if a machine receives 200 joules of energy and converts 150 joules into useful work, the efficiency is:

• Efficiency = (150 / 200) × 100 = 75%

This means the machine is 75% efficient, and the remaining 25% of energy is lost, usually as heat, sound, or friction.

No practical system can ever achieve 100% efficiency because some amount of energy is always lost during any energy transformation. These losses typically occur due to:

• Friction: Causes energy to be lost as heat in mechanical systems.
• Air Resistance: Converts some kinetic energy into thermal energy.
• Sound: Part of the input energy may be lost as sound energy.
• Heat Loss: Electrical and thermal systems lose energy in the form of heat.

Due to these unavoidable losses, not all the input energy is converted into useful output. Hence, the efficiency of any real system is always less than 100%.

Power is the rate at which work is done or energy is transferred over time. It indicates how fast or slow energy is being consumed or converted in a system.

• Formula: Power = Work / Time
• SI Unit: Watt (W)

One watt is equal to one joule per second.

To solve power-related problems, we use the formula:

• Power = Work / Time
• Or, Power = (Force × Distance) / Time

Example 1: A person lifts a 50 kg box to a height of 2 meters in 5 seconds. Find the power used.

• Work = m × g × h = 50 × 10 × 2 = 1000 J
• Power = 1000 / 5 = 200 Watts

Example 2: A machine does 1500 J of work in 3 seconds. What is its power output?

• Power = 1500 / 3 = 500 Watts

These examples show how to apply the power formula using known values of work and time.

The SI unit of power is the **watt (W)**. Power is defined as the rate at which work is done or energy is transferred.

• 1 Watt (W) is equal to 1 joule per second (1 J/s).
• That means if 1 joule of work is done in 1 second, the power used is 1 watt.

Other commonly used units of power include:

• Kilowatt (kW) = 1000 watts
• Horsepower (hp) ≈ 746 watts

To convert power from watts to horsepower, the following conversion factor is used:

• 1 horsepower (hp) ≈ 746 watts (W)

So, to convert watts to horsepower:

• Horsepower (hp) = Power (W) ÷ 746

Example:

• If a machine has a power of 1492 watts, then:
• Horsepower = 1492 ÷ 746 ≈ 2 hp

The kinetic molecular model explains that all matter is made up of tiny particles that are in constant motion. In solids, these particles are closely packed in fixed positions and can only vibrate, giving solids a definite shape and volume. In liquids, particles are still close but can slide past each other, allowing liquids to flow while maintaining a fixed volume but not a fixed shape. In gases, particles are far apart, move freely and quickly in all directions, and fill the entire space available, meaning gases have neither fixed shape nor volume.

Plasma is known as the fourth state of matter and is formed when gases are heated to extremely high temperatures or exposed to strong electromagnetic fields. In this state, atoms lose electrons and become a mixture of positively charged ions and free electrons. Plasma conducts electricity and responds strongly to magnetic fields. It is commonly found in lightning, stars (including the sun), neon signs, and fusion reactors.

Density is a physical property that describes how much mass is present in a given volume of a substance. It is used to compare how tightly matter is packed in different materials. Mathematically, density is calculated using the formula ρ = m / V, where m is the mass in kilograms and V is the volume in cubic meters. The SI unit of density is kilograms per cubic meter (kg/m³). For example, if a substance has a mass of 2 kg and a volume of 0.5 m³, its density would be 4 kg/m³. Substances with high density have more mass in a smaller space, like metals, whereas gases have low density due to their widely spaced particles.

The density of a substance depends on how closely its particles are packed together, which varies in each state of matter. Solids usually have the highest density because their particles are tightly packed in a fixed structure, making them heavy for their volume. Liquids have a lower density than solids because their particles are close but not rigid, allowing them to flow while still being relatively compact. Gases have the lowest density because their particles are far apart and move freely, resulting in a much lower mass per unit volume. This is why a balloon filled with gas is much lighter than a container of water or a solid object of the same size. Thus, density decreases from solids to liquids to gases.

Pressure is defined as the amount of force applied perpendicularly on a unit area of a surface. It shows how concentrated a force is over a specific area. The formula for pressure is:
Pressure (P) = Force (F) / Area (A)
The SI unit of pressure is the pascal (Pa), where 1 pascal equals 1 newton per square meter (N/m²).

Pressure depends on both the amount of force applied and the area over which it is spread. When force increases or the area decreases, pressure increases. For example:

• Standing on one foot puts more pressure on the ground than standing on both feet, because the same body weight acts on a smaller area.
• A sharp knife cuts more easily than a blunt one because the smaller surface area at the blade edge creates higher pressure.

These examples show how both force and area affect pressure in everyday life.

Atmospheric pressure is the force exerted by the weight of air molecules in the Earth's atmosphere on the surface of the Earth. It acts in all directions and is greatest at sea level where the air is densest. As you go higher above sea level, the air becomes thinner, and atmospheric pressure decreases.

Atmospheric pressure is commonly measured using a barometer, which contains a liquid column such as mercury. The height of the liquid in the tube reflects the pressure of the atmosphere pushing down on the liquid reservoir. A higher liquid column indicates higher atmospheric pressure, while a lower column indicates lower pressure.

As we move to higher altitudes above the Earth's surface, atmospheric pressure decreases. This happens because the number of air molecules becomes fewer with height, resulting in lower air density and less weight pressing down from above.

Changes in atmospheric pressure are often linked to weather changes. A falling atmospheric pressure usually signals stormy or rainy weather approaching, while rising pressure often indicates clear skies and dry conditions. Weather forecasters use pressure trends to predict short-term weather patterns.

Pascal’s law states that when pressure is applied to an enclosed fluid, the change in pressure is transmitted equally and undiminished throughout the fluid. This means that any force applied at one point in a fluid is felt equally at all other points within the container. The law only applies to incompressible fluids and enclosed systems. It forms the basis of many mechanical applications where pressure transmission is required. Examples include hydraulic brakes, car lifts, and other hydraulic machines. This law helps us understand how pressure works inside syringes, water pumps, and medical devices.

The pressure at any point beneath the surface of a liquid depends on three factors: the density of the liquid (ρ), the depth (h) from the surface, and gravitational acceleration (g). The relationship is given by the formula: P = ρgh. This means the deeper you go into a liquid, the more pressure you experience. Similarly, denser liquids exert more pressure than lighter ones at the same depth. For example, seawater exerts more pressure than freshwater at the same depth due to its higher density. This principle explains why submarines must be strong enough to withstand high pressures at great depths.

Pascal’s law is widely applied in hydraulic systems where force needs to be transmitted through liquids. In a hydraulic lift, a small force is applied to a small piston, which creates pressure in the fluid. This pressure is transmitted undiminished to a larger piston, generating a much greater force. This principle allows heavy vehicles to be lifted in car repair shops with very little input force. Similarly, hydraulic brakes in vehicles use fluid to transfer pressure from the brake pedal to the brake pads. These systems rely entirely on the uniform transmission of pressure described by Pascal’s law.

To solve problems involving pressure beneath a liquid, use the formula P = ρgh. Identify the liquid's density (ρ), the depth (h) at which pressure is being calculated, and use standard gravitational acceleration (g = 9.8 m/s²). Substitute the known values into the formula to find the pressure. Make sure units are consistent: density in kg/m³, depth in meters, and pressure in pascals (Pa). These problems often involve comparing pressure at different depths or in different liquids. For example, pressure at 5 meters depth in water (ρ = 1000 kg/m³) is: P = 1000 × 9.8 × 5 = 49,000 Pa.

Archimedes' principle states that any object fully or partially submerged in a fluid experiences an upward force, known as the buoyant force. This force is equal to the weight of the fluid displaced by the object. It explains why some objects float while others sink. If the buoyant force is greater than the object’s weight, it will float; if less, it will sink. This principle is used in designing ships, submarines, and hot air balloons. It also explains why we feel lighter when we are underwater — the water pushes us upward.

Archimedes’ principle can be used to find the density of an irregular object by measuring how much fluid it displaces when submerged. First, weigh the object in air to find its actual weight. Then submerge it fully in water and measure the loss in weight, which gives the buoyant force. This force equals the weight of the displaced fluid. From this, you can calculate the object’s volume and then use the formula: Density = Mass / Volume. This method is useful for irregular shapes that cannot be measured directly with rulers or formulas.

Upthrust, also known as buoyant force, is a vital concept in fluid mechanics. It is the upward force exerted by a liquid on an object that is either fully or partially submerged in it. This force acts in the opposite direction to the weight of the object. The significance of upthrust lies in its role in determining whether an object will float or sink. If the upthrust is greater than or equal to the object’s weight, the object floats; if it is less, the object sinks. Upthrust is responsible for the floating of ships, icebergs, and even humans in water. This principle is used in designing boats, submarines, and hydraulic devices to ensure proper buoyancy and stability.

The principle of floatation explains why objects float or sink in a fluid. It states that an object will float if the upthrust (or buoyant force) acting on it is equal to or greater than its weight. Upthrust is the upward force exerted by the fluid when an object is submerged. When this force balances the weight of the object, it stays afloat. If the object is heavier than the upthrust, it sinks. This principle helps in understanding the floating of ships, boats, and even icebergs. Designers of watercraft use this principle to ensure proper balance and safety in water navigation.

Elasticity is the property of a material that enables it to regain its original shape and size after the removal of a deforming force. Materials that exhibit this property are called elastic materials, such as rubber and springs. When an elastic object is stretched, compressed, or bent, it stores energy in the form of potential energy. Once the force is removed, the stored energy helps it return to its original form. Elasticity is an important concept in physics and engineering, as it helps in designing materials that can withstand stress and return to their initial form without permanent deformation.

When a force is applied to a body, it may lead to a change in the size or shape of the object. This deformation depends on the nature of the material and the magnitude of the applied force. For instance, stretching a rubber band changes its length, while pressing a sponge changes its shape. In elastic materials, the deformation is temporary and the object returns to its original state once the force is removed. However, if the force is too great or the material is non-elastic, the deformation may become permanent. This behavior is essential in understanding stress, strain, and material strength.

Stress is defined as the internal force exerted per unit area within a material when an external force is applied. It is measured in Pascals (Pa). Strain, on the other hand, is the measure of deformation experienced by the body in the direction of the applied force, expressed as a ratio of change in dimension to the original dimension. Young’s modulus is a property of materials that quantifies their stiffness. It is defined as the ratio of stress to strain in the region where Hooke’s law holds. A high Young’s modulus indicates that a material is stiff and resists deformation, while a low modulus indicates flexibility.

Hooke’s law states that the extension or compression of an elastic object, like a spring, is directly proportional to the force applied to it, provided the material's elastic limit is not exceeded. Mathematically, it is expressed as F = kx, where F is the applied force, x is the extension or compression, and k is the spring constant. This law helps us understand how materials respond to forces and is crucial in the design of mechanical systems. It only applies to materials within their elastic range, meaning they return to their original shape after the force is removed.

The elastic limit is the maximum amount of stress a material can withstand while still returning to its original shape once the force is removed. According to Hooke’s law, stress is proportional to strain up to this limit. When a material is stretched beyond its elastic limit, it undergoes plastic deformation, meaning it will not return to its original shape. This limit defines the boundary between reversible (elastic) and irreversible (plastic) behavior of a material. Engineers and designers must consider the elastic limit when selecting materials to ensure safety and durability in structures and devices.

Heat and temperature are closely related but distinctly different concepts in physics. Temperature refers to the measure of the average kinetic energy of the molecules or particles in a substance. It indicates how hot or cold an object is and is measured in degrees Celsius (°C), Fahrenheit (°F), or Kelvin (K). On the other hand, heat is the form of energy that is transferred between two objects due to a temperature difference. Heat flows from a hotter object to a cooler one and is measured in joules (J) or calories (cal). Unlike temperature, which is a scalar quantity and describes a state, heat represents energy in transit and depends on the mass, specific heat, and temperature change of a substance. Temperature remains constant during a phase change, while heat continues to be absorbed or released.

Thermometric materials such as mercury and alcohol are selected based on certain basic properties. These include uniform and predictable thermal expansion, visibility in a capillary tube, non-adhesion to glass, and a wide operating temperature range. Mercury is ideal due to its consistent expansion rate, shiny appearance, and non-wettability. Alcohol, on the other hand, is used in very cold regions due to its lower freezing point. It can be dyed for visibility and expands more than mercury, making it suitable for precise readings at lower temperatures.

Temperature conversion between different scales is essential for scientific and practical use. To convert Celsius to Fahrenheit, the formula is F = (9/5 × C) + 32. To convert Fahrenheit to Celsius, use C = (5/9) × (F - 32). For converting Celsius to Kelvin, simply add 273.15 to the Celsius temperature, i.e., K = C + 273.15. Similarly, to convert Kelvin to Celsius, subtract 273.15 from Kelvin. These formulas allow accurate conversion between temperature scales used globally.

A rise in the temperature of a body indicates an increase in its internal energy. This internal energy is mainly the kinetic energy of its particles. When a substance absorbs heat, the particles move faster, increasing their kinetic energy, which manifests as a rise in temperature. Therefore, the temperature of a body is directly related to the average kinetic energy of its molecules. This principle helps explain heating processes at the molecular level.

Liquid-in-glass thermometers are simple to use, cost-effective, and provide accurate readings within a moderate temperature range. They are easy to read and do not require external power sources. However, they are fragile due to the glass construction and not suitable for extreme high or low temperatures. Thermocouple thermometers, in contrast, are durable, respond quickly, and can measure a very wide range of temperatures with high precision. The downside is they are more expensive, require calibration, and may need electronic support to display readings.

Heat capacity is defined as the quantity of heat energy required to raise the temperature of a whole object or substance by 1°C. It depends on the mass and material of the object. The greater the heat capacity, the more heat is needed to change its temperature. Specific heat capacity, on the other hand, is a property of a material that represents the amount of heat needed to raise the temperature of 1 kilogram of the substance by 1°C (or 1 K). It is denoted by ‘c’ and has the unit J/(kg·°C). Unlike heat capacity, specific heat capacity is independent of the quantity of the material and is useful for comparing thermal properties of different materials.

Word problems related to specific heat capacity involve calculating the amount of heat energy required to change the temperature of a substance. The formula used is Q = mcΔT, where Q is the heat energy (in joules), m is the mass (in kilograms), c is the specific heat capacity, and ΔT is the temperature change. For example, if 2 kg of water is heated from 20°C to 50°C, and the specific heat of water is 4200 J/kg°C, then Q = 2 × 4200 × (50 - 20) = 252,000 J. These problems help students understand the relationship between heat, mass, temperature change, and the thermal properties of different substances.

Heat of fusion is the amount of thermal energy required to convert a solid into a liquid at its melting point without changing its temperature. It is needed to overcome the forces holding the particles together in the solid state. For example, ice requires heat of fusion to become water at 0°C. On the other hand, heat of vaporization is the amount of heat energy required to convert a liquid into vapor at its boiling point, also without any change in temperature. This energy is used to break the intermolecular bonds in the liquid state. For example, water requires heat of vaporization to become steam at 100°C. Both processes are crucial in understanding phase changes and energy transfer in thermodynamics.

The heat of fusion and heat of vaporization can be determined using a temperature-time graph during the phase change process. When heat is continuously supplied to ice, its temperature rises until it reaches 0°C. At this point, the temperature remains constant while ice melts into water, indicating the heat of fusion is being absorbed. Similarly, when water reaches 100°C, it starts boiling, and the temperature again stays constant while water changes into steam, showing the heat of vaporization is being absorbed. These flat, horizontal regions (plateaus) on the graph show that energy is used for changing the state and not for raising the temperature. By measuring the time taken and knowing the heat supplied per unit time, the total energy (Q = m × L) can be calculated for both fusion and vaporization.

The formula to solve latent heat problems is Q = m × L, where Q is the heat energy (in joules), m is the mass of the substance (in kg or g), and L is the specific latent heat (in J/kg or J/g). For example, to melt 300 g of ice at 0°C, and knowing the latent heat of fusion of ice is 334 J/g, the heat needed is Q = 300 × 334 = 100,200 J. Similarly, to convert 250 g of water at 100°C into steam, and using latent heat of vaporization of 2260 J/g, the energy required is Q = 250 × 2260 = 565,000 J. It is important to keep the units consistent and identify whether the substance is melting or boiling to use the correct latent heat constant.

Evaporation is the process by which molecules at the surface of a liquid gain enough kinetic energy to overcome the attractive forces of neighboring molecules and escape into the gas phase.

Boiling occurs when the vapor pressure of a liquid equals the atmospheric pressure, resulting in rapid vaporization throughout the liquid. Evaporation occurs at the surface of a liquid and can occur at any temperature below the boiling point.

Evaporation causes cooling because the molecules with higher kinetic energy are more likely to leave the liquid phase, taking away energy in the form of latent heat. This results in a decrease in the average kinetic energy of the remaining molecules, leading to a decrease in temperature.

Factors that influence surface evaporation include temperature, surface area, humidity, and airflow. Higher temperatures, larger surface areas, lower humidity, and increased airflow typically lead to faster evaporation rates.

Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. In solids, this phenomenon is explained in two ways: Linear expansion refers to the increase in length of a solid material when it is heated. It is observed in long objects like rods and rails. Volumetric expansion refers to the increase in the total volume of a solid due to heating. This is more prominent in three-dimensional objects and is calculated using the coefficient of volumetric expansion. Both types of expansion are important in real-world applications such as construction, machinery, and transportation.

Thermal expansion of liquids is more noticeable than that of solids. Real expansion is the actual increase in the volume of the liquid when it is heated. However, this is not always directly observed because the container holding the liquid also expands. Apparent expansion is the expansion observed by the rise of liquid level in a container and is less than the real expansion. This is because part of the liquid expansion is offset by the expansion of the container itself. The relationship between real and apparent expansion helps in accurately measuring the properties of liquids in practical applications.

Thermal energy is the internal energy of a system that results from the motion of its particles. It is associated with the random kinetic energy of atoms and molecules within a substance. When an object is heated, its particles move more rapidly, increasing its internal energy and hence its thermal energy. This change in internal energy leads to temperature rise or a change in state.

In solids, heat transfer occurs through the process of conduction. The atoms and molecules vibrate more intensely when heated, and these vibrations are passed from one particle to another. In metals, free electrons move throughout the structure and help transfer heat more efficiently by colliding with other electrons and atoms, carrying energy from the hot end to the cooler end.

Thermal conductivity is the property of a material that indicates its ability to conduct heat. It is defined as the quantity of heat that passes through a unit area of a material in a unit time for a unit temperature gradient. Materials with high thermal conductivity, like copper, allow heat to pass through quickly, while materials with low conductivity, like wood, do not.

The transfer of heat through solid conductors is affected by several factors:

• Thermal conductivity: Materials with higher conductivity transfer heat faster.
• Temperature gradient: A greater difference in temperature increases the rate of heat transfer.
• Cross-sectional area: A larger area allows more heat to flow.
• Length of the conductor: A shorter length results in faster heat transfer.

Word problems based on thermal conductivity involve using the formula:
Q = (k × A × ΔT × t) / L
Where:

• Q = Heat transferred (Joules)
• k = Thermal conductivity of the material
• A = Cross-sectional area
• ΔT = Temperature difference
• t = Time
• L = Length of the conductor

Solving such problems involves substituting known values to calculate the unknown quantity, usually the amount of heat transferred or time required.

Good conductors of heat are materials that allow heat to pass through them quickly. Examples include metals like copper, silver, and aluminum. Bad conductors, or insulators, are materials that resist the flow of heat. Examples of insulators include wood, plastic, rubber, and glass. These materials are used where heat retention or isolation is needed.

Good conductors are used where efficient heat transfer is required. Examples include:

• Cooking pots and pans (usually made of aluminum or copper)
• Electrical appliances and heat exchangers
• Ironing boards and radiators

Bad conductors (insulators) are used to prevent heat loss or gain. Examples include:

• Building insulation (glass wool, foam)
• Thermos flasks and coolers
• Plastic handles of cooking utensils
• Winter clothing (wool, synthetic fiber)

Insulation reduces energy transfer by conduction by using materials that are poor conductors of heat. These materials, such as foam, fiberglass, wool, or plastic, have very low thermal conductivity, meaning they do not allow heat to flow easily through them. When placed between two regions of different temperatures, the insulating layer acts as a barrier that slows down the movement of thermal energy. This is particularly useful in maintaining desired temperatures in homes, refrigerators, and thermos flasks. The effectiveness of insulation depends on its thickness, density, and the thermal conductivity of the material used. By minimizing heat loss or gain, insulation helps in energy conservation and improves energy efficiency in various systems.

Convection currents in fluids occur as a result of density differences caused by temperature variations. When a fluid, such as water or air, is heated, the particles gain energy and move apart, decreasing the fluid's density. This lighter, warmer fluid rises, and in its place, the cooler and denser fluid sinks. This sets up a circular flow known as a convection current. The cycle continues as the rising warm fluid cools and sinks again. This process effectively transfers heat throughout the fluid and plays a vital role in both natural phenomena and man-made systems. For example, convection currents help distribute heat in oceans, the atmosphere, and even in heating systems in buildings.

Heat transfer by convection is commonly observed in many everyday situations. For instance, in a heated room, warm air from a radiator rises and circulates, spreading warmth throughout the room. Another example is boiling water in a pot, where hot water from the bottom rises and cooler water sinks, creating a convection loop. Similarly, in air conditioners, cooler air sinks while warm air rises, allowing effective temperature regulation. Ocean currents and wind patterns are also driven by convection, transporting heat across the globe. These examples show how convection plays a key role in the natural and artificial movement of heat.

Radiation is the transfer of energy through electromagnetic waves or photons. Unlike conduction and convection, radiation does not require a medium and can occur through a vacuum. All objects emit radiation continuously, and the amount of radiation depends on the object's temperature and surface characteristics. Hotter objects emit more radiation, and dark, matte surfaces emit and absorb radiation more effectively than light, shiny surfaces.

The rate of energy transfer through radiation is influenced by several factors:

• Color and texture: Dark-colored and rough-textured surfaces absorb and emit more heat compared to light-colored and smooth surfaces.
• Surface temperature: Higher surface temperatures increase the rate at which energy is radiated.
• Surface area: A larger surface area allows more radiation to be emitted or absorbed, increasing the overall rate of energy transfer.

The greenhouse effect refers to the warming of the Earth's surface due to the trapping of heat by greenhouse gases in the atmosphere. Solar radiation from the Sun passes through the Earth's atmosphere and warms the surface. The Earth then emits this energy as infrared radiation (heat). Greenhouse gases like carbon dioxide, methane, and water vapor absorb and re-radiate this heat, preventing it from escaping into space. This natural process maintains the Earth's temperature at a level suitable for life. However, excessive greenhouse gas emissions from human activities are intensifying the effect, leading to global warming and climate change.