Class 9 Notes

Class 9 Science Notes Chapter 10 (Chapter 10) – Examplar Problem (English) Book

Philoid

Philoid

— 7 min read

Examplar Problem (English)
Alright class, let's focus on Chapter 10: Gravitation from your NCERT Exemplar. This is a crucial chapter, not just for your school exams but also forms the basis for many concepts tested in government recruitment exams. Pay close attention to the details.

Chapter 10: Gravitation - Detailed Notes for Competitive Exams

1. Universal Law of Gravitation (Newton's Law of Gravitation):

  • Statement: 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 their centers.
  • Mathematical Expression:
    Consider two objects A and B with masses M and m respectively, separated by a distance 'd' (measured from their centers). The force of attraction (F) between them is:
    F ∝ M * m
    F ∝ 1 / d²
    Combining these, F ∝ (M * m) / d²
    Therefore, F = G * (M * m) / d²
  • G - Universal Gravitational Constant:
    • It is the proportionality constant in the formula.
    • Its value is constant throughout the universe.
    • G = 6.673 × 10⁻¹¹ N m² kg⁻² (Remember the value and the unit).
    • The law is called 'universal' because it applies to all objects, irrespective of their size, shape, or the medium between them (celestial bodies, terrestrial objects).
  • Key Points:
    • Gravitational force is always attractive.
    • It's a central force (acts along the line joining the centers).
    • It's a conservative force.
    • It's the weakest of the fundamental forces but dominates on a large scale (like planets, stars) due to the large masses involved.
    • It obeys Newton's Third Law (Force exerted by A on B is equal and opposite to the force exerted by B on A).

2. 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 tides due to the Moon and the Sun.

3. Free Fall:

  • Definition: When an object falls towards the Earth solely under the influence of Earth's gravitational force (neglecting air resistance), it is said to be in free fall.
  • Acceleration during Free Fall: The object experiences a constant acceleration directed towards the center of the Earth. This is called acceleration due to gravity (g).
  • Value of g: The standard value of 'g' on the surface of the Earth is approximately 9.8 m/s². This means the velocity of a freely falling object increases by 9.8 m/s every second.
  • Relation between g and G:
    Consider an object of mass 'm' on the surface of the Earth (mass M, radius R). The force on the object is F = G * (M * m) / R².
    Also, according to Newton's Second Law, F = m * g.
    Equating the two, m * g = G * (M * m) / R²
    Therefore, g = G * M / R²
  • Key Points:
    • 'g' is independent of the mass ('m') of the falling object. A heavy object and a light object dropped from the same height will reach the ground simultaneously in a vacuum.
    • 'g' depends on the mass (M) and radius (R) of the planet/celestial body.

4. Variation in the Value of 'g':

  • Altitude: 'g' decreases as we go up from the surface of the Earth (g ∝ 1 / (R+h)², where h is the height above the surface).
  • Depth: 'g' decreases as we go down below the surface of the Earth. At the center of the Earth, g = 0. (g' = g * (1 - d/R), where d is depth).
  • Shape of the Earth: The Earth is not a perfect sphere; it's flattened at the poles and bulged at the equator. Since the equatorial radius is greater than the polar radius, 'g' is minimum at the equator and maximum at the poles.
  • Rotation of the Earth: The rotation also causes 'g' to be slightly less at the equator than at the poles.

5. Mass and Weight:

  • Mass (m):
    • Definition: The measure of the inertia of an object; the amount of matter contained in it.
    • Unit: Kilogram (kg) (SI unit).
    • Nature: Scalar quantity.
    • Constancy: Mass of an object is constant everywhere in the universe. It does not change with location.
    • Measurement: Measured using a beam balance (comparing masses).
  • Weight (W):
    • Definition: The force with which an object is attracted towards the center of the Earth (or any celestial body). It's the gravitational force acting on the object.
    • Formula: W = m * g
    • Unit: Newton (N) (SI unit). Also sometimes measured in kilogram-force (kgf). 1 kgf = 9.8 N.
    • Nature: Vector quantity (directed towards the center of the Earth).
    • Variability: Weight changes with the value of 'g'. An object's weight is different on different planets or even at different locations on Earth (poles vs. equator, altitude).
    • Measurement: Measured using a spring balance.
  • Weight on the Moon: The Moon's mass is less, and its radius is smaller than Earth's. The acceleration due to gravity on the Moon (g_moon) is about 1/6th of that on Earth (g_earth).
    g_moon ≈ (1/6) * g_earth
    Therefore, Weight_moon = m * g_moon = m * (1/6) * g_earth = (1/6) * Weight_earth.
    An object's weight on the Moon is one-sixth its weight on Earth. Its mass remains the same.

6. Thrust and Pressure:

  • Thrust:
    • Definition: The force acting perpendicularly on a surface.
    • Unit: Newton (N) (SI unit). It's simply a force.
  • Pressure (P):
    • Definition: The thrust (perpendicular force) acting per unit area of a surface.
    • Formula: Pressure (P) = Thrust / Area = F / A
    • Unit: Pascal (Pa) (SI unit). 1 Pa = 1 N/m². Other units include bar, atm (atmosphere).
    • Nature: Scalar quantity.
  • Key Points & Applications:
    • Pressure is inversely proportional to the area over which the force acts (P ∝ 1/A).
    • Sharp knives cut better (small area, high pressure).
    • Wide straps of bags are comfortable (large area, low pressure).
    • Tractor tires are wide (large area, low pressure on soft ground).
    • Foundations of buildings are wide (large area, low pressure on the ground).

7. Pressure in Fluids (Liquids and Gases):

  • Definition: Fluids exert pressure on the base and walls of their container. They also exert pressure in all directions at any given point within the fluid.
  • Pressure due to a Liquid Column: The pressure exerted by a column of liquid of height 'h', density 'ρ' (rho), at a point is given by:
    P = h * ρ * g
  • Key Points:
    • Pressure increases with depth inside a liquid.
    • Pressure at a given depth is the same in all directions.
    • Pressure at the same depth is equal in a static, connected liquid (Pascal's Law application).
    • Liquids seek their own level.

8. Buoyancy:

  • Definition: When an object is immersed partially or wholly in a fluid (liquid or gas), it experiences an upward force exerted by the fluid. This upward force is called the buoyant force or upthrust.
  • Cause: Buoyancy arises due to the pressure difference in the fluid. The pressure at the bottom surface of the object (deeper in the fluid) is greater than the pressure at the top surface. This pressure difference results in a net upward force.
  • Factors Affecting Buoyant Force:
    • Volume of the object immersed in the fluid (Larger the volume immersed, greater the buoyant force).
    • Density of the fluid (Denser the fluid, greater the buoyant force).
  • Floating and Sinking:
    • An object sinks if its weight (W) is greater than the buoyant force (Fb). This happens when the density of the object (ρ_object) is greater than the density of the fluid (ρ_fluid).
    • An object floats if its weight (W) is equal to or less than the buoyant force (Fb). This happens when the density of the object (ρ_object) is less than or equal to the density of the fluid (ρ_fluid).
    • When floating, Weight of object = Buoyant Force = Weight of the fluid displaced by the immersed part of the object.

9. 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.
  • Mathematical Expression: Buoyant Force (Fb) = Weight of the fluid displaced
    Fb = (Volume of displaced fluid) * (Density of fluid) * g
    Fb = V_displaced * ρ_fluid * g
  • Applications:
    • Designing ships and submarines.
    • Determining the relative density of substances.
    • Lactometers (to check milk purity).
    • Hydrometers (to measure the density of liquids).

10. Density and Relative Density:

  • Density (ρ):
    • Definition: Mass per unit volume of a substance.
    • Formula: Density (ρ) = Mass (m) / Volume (V)
    • Unit: kg/m³ (SI unit). Also g/cm³. (1 g/cm³ = 1000 kg/m³)
  • Relative Density (R.D.):
    • Definition: The ratio of the density of a substance to the density of water (usually at 4°C, where water has maximum density).
    • Formula: Relative Density = Density of Substance / Density of Water
    • Unit: It is a pure ratio, hence it has no units.
  • Key Points:
    • Relative density helps compare the density of a substance with water.
    • If R.D. > 1, the substance is denser than water (will sink).
    • If R.D. < 1, the substance is less dense than water (will float).
    • If R.D. = 1, the substance has the same density as water.
    • Density of water = 1000 kg/m³ or 1 g/cm³.

Multiple Choice Questions (MCQs) for Practice:

  1. The value of acceleration due to gravity (g) is:
    (a) Maximum at the equator
    (b) Maximum at the poles
    (c) Same everywhere on the surface of Earth
    (d) Maximum at the center of the Earth

  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 the Moon's surface is W. Its weight on the Earth's surface would be approximately:
    (a) W / 6
    (b) 6 W
    (c) W
    (d) W / 36

  4. A body is weighed in a liquid using a spring balance. The reading on the spring balance will be:
    (a) Equal to the actual weight of the body
    (b) More than the actual weight of the body
    (c) Less than the actual weight of the body
    (d) Dependent on the density of the spring material

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

  6. According to Archimedes' principle, the buoyant force acting on an object is equal to:
    (a) The volume of the fluid displaced
    (b) The mass of the fluid displaced
    (c) The weight of the fluid displaced
    (d) The density of the fluid displaced

  7. If the distance between two masses is doubled, the gravitational attraction between them:
    (a) Is doubled
    (b) Becomes four times
    (c) Is reduced to half
    (d) Is reduced to one-fourth

  8. A block of wood floats in water with two-thirds of its volume submerged. The relative density of wood is:
    (a) 1/3
    (b) 2/3
    (c) 1
    (d) 3/2

  9. The universal gravitational constant (G) has the unit:
    (a) N m kg⁻¹
    (b) N m² kg⁻²
    (c) N m⁻² kg²
    (d) N kg m⁻¹

  10. 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

Answer Key for MCQs:

  1. (b)
  2. (a)
  3. (b)
  4. (c)
  5. (c)
  6. (c)
  7. (d)
  8. (b) [Hint: For floating, Weight = Buoyant Force => V_obj * ρ_obj * g = V_submerged * ρ_water * g. ρ_obj / ρ_water = V_submerged / V_obj. Relative Density = 2/3]
  9. (b)
  10. (a) [Hint: Apparent weight = Actual weight - Buoyant force. Buoyant force = Actual weight - Apparent weight = 10 N - 8 N = 2 N. By Archimedes' principle, Buoyant force = Weight of liquid displaced.]

Study these notes thoroughly. Remember the definitions, formulas, units, and the reasoning behind the concepts, especially the variations in 'g' and the principles of buoyancy. Good luck with your preparation!

Read more