Class 9 Science Notes Chapter 10 (Gravitation) – Science Book

Alright class, let's focus on Chapter 10, 'Gravitation'. This is a fundamental chapter, not just for your Class 9 understanding, but also because its concepts frequently appear in various government exams. Pay close attention to the definitions, laws, and formulas.

Chapter 10: Gravitation - Detailed Notes for Exam Preparation

1. Introduction to Gravitation

• Gravitation is the fundamental force of attraction acting between any two objects with mass in the universe.
• It's the force that holds galaxies together, keeps planets in orbit around stars, the Moon around the Earth, and pulls objects towards the Earth.

2. Universal Law of Gravitation (Newton's Law of Gravitation)

• Statement: Every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• Formula:
  F = G * (m1 * m2) / d²
  Where:
  • F = Gravitational force between the two objects
  • G = Universal Gravitational Constant
  • m1 = Mass of the first object
  • m2 = Mass of the second object
  • d = Distance between the centers of the two objects
• Key Points:
  • The force is always attractive.
  • It acts along the line joining the centers of the two masses.
  • It is a universal law – applicable to all objects, irrespective of their size, shape, or the medium between them.
• Universal Gravitational Constant (G):
  • It is the proportionality constant in the formula.
  • Its value is constant throughout the universe.
  • Accepted value: G = 6.673 × 10⁻¹¹ N m²/kg²
  • Its SI unit is N m²/kg². (This unit is often asked in exams).
  • The small value of G explains why gravitational force between everyday objects is negligible.

3. Importance of the Universal Law of Gravitation

• Explains the force that binds us to the Earth.
• Explains the motion of the Moon around the Earth.
• Explains the motion of planets around the Sun.
• Explains the occurrence of tides (due to the gravitational pull of the Moon and the Sun on Earth's water).

4. Free Fall

• Definition: Whenever objects fall towards the Earth under the influence of Earth's gravitational force alone (neglecting air resistance), they are said to be in free fall.
• Acceleration Due to Gravity (g):
  • During free fall, objects experience an acceleration directed towards the center of the Earth. This is called acceleration due to gravity, denoted by g.
  • It is (ideally) the same for all objects, regardless of their mass (as observed by Galileo).
  • Value: The standard value of g near the Earth's surface is approximately 9.8 m/s². For calculation purposes, it's sometimes taken as 10 m/s².
  • Variation: The value of g is not strictly constant. It:
    • Decreases with increasing altitude (height above Earth's surface).
    • Decreases with increasing depth below Earth's surface.
    • Is slightly greater at the poles than at the equator (because Earth is not a perfect sphere; it's flattened at the poles and bulged at the equator, making the polar radius smaller than the equatorial radius).
  • Relation between g and G:
    g = G * M / R²
    Where:
    • G = Universal Gravitational Constant
    • M = Mass of the Earth
    • R = Radius of the Earth
• Equations of Motion for Freely Falling Bodies:
  • These are derived from the standard equations of motion by replacing acceleration a with g (or -g if motion is upwards against gravity).
  • v = u + gt
  • h = ut + ½ gt² (Here h is used for vertical distance instead of s)
  • v² = u² + 2gh
  • Sign Convention: Usually, downward direction (direction of g) is taken as positive. If an object is thrown upwards, its initial velocity u is positive, but g acts downwards, so it's often taken as negative in the equations for upward motion.

5. Mass

• Definition: Mass of an object is the measure of its inertia. It represents the amount of matter contained in the object.
• SI Unit: Kilogram (kg)
• Properties:
  • It is a scalar quantity.
  • It remains constant everywhere in the universe.
  • It can never be zero.
  • It is measured using a beam balance or common balance.

6. Weight

• Definition: Weight of an object is the force with which it is attracted towards the center of the Earth (or any celestial body).
• Formula: W = m × g
  Since weight is a force, its direction is always towards the center of the Earth.
• SI Unit: Newton (N) (Same as the unit of force).
• Properties:
  • It is a vector quantity.
  • It varies from place to place because the value of g varies.
  • It can be zero (e.g., in deep space, far from any gravitational influence, where g ≈ 0). This condition is often referred to as weightlessness.
  • It is measured using a spring balance.

Comparison: Mass vs. Weight

7. Weight of an Object on the Moon

• The Moon has less mass and a smaller radius than the Earth. Therefore, the acceleration due to gravity on the Moon (g_moon) is less than that on Earth (g_earth).
• g_moon is approximately 1/6 of g_earth.
• Therefore, the weight of an object on the Moon is about 1/6 of its weight on Earth.
  W_moon = (1/6) * W_earth
• Note: The mass of the object remains the same on the Moon and the Earth.

8. Thrust and Pressure

• Thrust: The force acting on an object perpendicular to its surface.
  • SI Unit: Newton (N)
• Pressure: The thrust (perpendicular force) acting per unit area.
  • Formula: Pressure (P) = Thrust (Force, F) / Area (A)
  • SI Unit: Pascal (Pa) or N/m². (1 Pa = 1 N/m²)
• Key Concepts:
  • Pressure is inversely proportional to the area over which the force acts. Smaller the area, larger the pressure for the same force (e.g., sharp knife, pointed nail).
  • Larger the area, smaller the pressure for the same force (e.g., wide straps of school bags, broad foundations of buildings, wide tires of tractors, skis on snow).

9. Pressure in Fluids (Liquids and Gases)

• Fluids exert pressure on the base and walls of the container they are in.
• Pressure exerted by a fluid at a point acts equally in all directions.
• Pressure exerted by a liquid column depends on:
  • Height of the liquid column (h)
  • Density of the liquid (ρ - rho)
  • Acceleration due to gravity (g)
  • Formula: P = hρg

10. Buoyancy (Upthrust)

• Definition: When an object is immersed partially or fully in a fluid (liquid or gas), it experiences an upward force called the buoyant force or upthrust.
• Cause: This force arises due to the pressure difference exerted by the fluid on the lower and upper surfaces of the submerged object (pressure is greater at greater depth).
• Factors Affecting Buoyant Force:
  • Volume of the object submerged: Larger the volume submerged, greater the buoyant force.
  • Density of the fluid: Higher the density of the fluid, greater the buoyant force.
• Floating/Sinking:
  • An object floats if the buoyant force is equal to or greater than its weight.
  • An object sinks if its weight is greater than the buoyant force.
  • This can also be compared using densities: An object sinks if its density is greater than the fluid's density, and floats if its density is less than the fluid's density.

11. Archimedes' Principle

• Statement: When a body is immersed fully or partially in a fluid, it experiences an upward force (buoyant force) that is equal to the weight of the fluid displaced by it.
• Applications:
  • Designing ships and submarines (they displace a large volume of water, making the buoyant force large enough to support their weight).
  • Lactometers (used to determine the purity of milk).
  • Hydrometers (used to determine the density of liquids).

12. Relative Density

• Definition: It is the ratio of the density of a substance to the density of water (usually taken at 4°C).
• Formula: Relative Density = Density of Substance / Density of Water
• Key Points:
  • It is a pure ratio, so it has no units.
  • Density of water is approximately 1000 kg/m³ or 1 g/cm³.
  • Significance:
    • If Relative Density > 1, the substance is denser than water and will sink.
    • If Relative Density < 1, the substance is less dense than water and will float.
    • If Relative Density = 1, the substance has the same density as water and will float just fully submerged.

Multiple Choice Questions (MCQs)

1. The value of the universal gravitational constant 'G' depends upon:
   a) Mass of the objects
   b) Distance between the objects
   c) Medium between the objects
   d) None of the above

2. Two objects of different masses falling freely near the surface of the moon would:
   a) have same velocities at any instant
   b) have different accelerations
   c) experience forces of same magnitude
   d) undergo a change in their inertia

3. The weight of an object on Earth is W. Its weight on a planet having double the radius and half the mass of Earth would be:
   a) W/8
   b) W/4
   c) W/2
   d) W

4. A boy is whirling a stone tied with a string in a horizontal circular path. If the string breaks, the stone:
   a) will continue to move in the circular path
   b) will move along a straight line towards the centre of the circular path
   c) will move along a straight line tangential to the circular path
   d) will move along a straight line perpendicular to the circular path away from the boy

5. The pressure exerted by a liquid column at the bottom of a container depends on:
   a) Area of the base of the container
   b) Shape of the container
   c) Height of the liquid column
   d) All of the above

6. An object weighs 10 N in air. When immersed fully in water, it weighs only 8 N. The weight of the liquid displaced by the object will be:
   a) 2 N
   b) 8 N
   c) 10 N
   d) 12 N

7. The SI unit of pressure is:
   a) N m²
   b) N/m
   c) N/m²
   d) N m

8. Which of the following statements is true regarding mass and weight?
   a) Mass varies with location, while weight is constant.
   b) Mass is a vector quantity, while weight is a scalar quantity.
   c) Mass is measured using a spring balance.
   d) Weight depends on the acceleration due to gravity 'g'.

9. The relative density of silver is 10.8. The density of water is 1000 kg/m³. What is the density of silver in SI units?
   a) 10.8 kg/m³
   b) 108 kg/m³
   c) 1080 kg/m³
   d) 10800 kg/m³

10. According to the universal law of gravitation, the gravitational force between two bodies is:
    a) Directly proportional to the distance between them
    b) Inversely proportional to the product of their masses
    c) Directly proportional to the product of their masses
    d) Inversely proportional to the sum of their masses

Answers to MCQs:

1. d) None of the above (G is a universal constant)
2. a) have same velocities at any instant (because acceleration due to gravity on the moon is constant for all objects, neglecting air resistance which is absent anyway)
3. a) W/8 (g = GM/R². New g' = G(M/2)/(2R)² = G(M/2)/(4R²) = (1/8) GM/R² = g/8. So, new weight W' = mg' = mg/8 = W/8)
4. c) will move along a straight line tangential to the circular path (due to inertia of direction)
5. c) Height of the liquid column (P = hρg)
6. a) 2 N (By Archimedes' Principle, Buoyant force = Weight in air - Weight in water = 10 N - 8 N = 2 N. Buoyant force = Weight of liquid displaced)
7. c) N/m² (Pascal)
8. d) Weight depends on the acceleration due to gravity 'g'.
9. d) 10800 kg/m³ (Relative Density = Density of substance / Density of water => Density of substance = Relative Density × Density of water = 10.8 × 1000 kg/m³ = 10800 kg/m³)
10. c) Directly proportional to the product of their masses (F ∝ m1*m2)

Make sure you revise these concepts thoroughly. Understanding the relationship between formulas and the physical phenomena they describe is key for competitive exams. Good luck!