Motion and Force:

  • Objects require a force to change their speed or direction of motion.
  • Objects like an apple falling towards the earth or planets orbiting the Sun are influenced by force.
  • This force is called gravitational force, and it acts on all objects in the universe.

Gravitation:

  • Isaac Newton, after observing an apple falling, deduced that the same force causing the apple to fall must be responsible for the moon’s motion around the Earth.
  • The force of gravitation pulls objects toward the Earth. Similarly, the Earth attracts other objects, including the moon.

Centripetal Force:

  • When an object moves in a circular path, like a stone tied to a thread and whirled around, it experiences a force towards the center of the circle, called centripetal force. This is what keeps the moon in orbit around Earth.

Universal Law of Gravitation:

  • Every object in the universe attracts every other object. The strength of the force is:
    • Directly proportional to the product of the masses of the two objects.
    • Inversely proportional to the square of the distance between them.
  • The formula for the gravitational force is:
    • F= G⋅M⋅m/d2​ where:
      • G is the universal gravitational constant,
      • M and m are the masses of the two objects,
      • d is the distance between them.

Gravitational Force Between Earth and Moon:

  • The force exerted by the Earth on the moon is calculated using the universal law of gravitation formula.
  • Example: For Earth and the Moon, the force comes out to be 2.02×1020N.

Importance of Universal Law of Gravitation:

  • This law explains several phenomena:
    1. The force that keeps us grounded on Earth.
    2. The motion of the moon around Earth.
    3. The motion of planets around the Sun.
    4. The tides caused by the gravitational interaction of the Moon and the Sun.

Free Fall:

  • When an object falls towards the Earth under the influence of gravity alone, it is said to be in free fall.
  • The acceleration experienced by objects in free fall is called acceleration due to gravity (denoted as g).

Calculation of g:

  • The formula for g is derived using the universal law of gravitation. The value of g near the Earth’s surface is approximately 9.8 m/s2.

Motion of Objects Under Gravitational Force:

  • All objects fall at the same rate under gravity, regardless of their mass, in the absence of air resistance. This was demonstrated by Galileo.

Equations of Motion:

  • The equations of motion for objects in free fall (or any uniformly accelerated motion) are: v=u+at, s=ut+ ½ at2, v2=u2+2as, where:
    • u is initial velocity,
    • v is final velocity,
    • a is acceleration,
    • s is displacement,
    • t is time.

Weight:

  • Weight is the force with which an object is attracted towards the Earth. It depends on the mass of the object and the value of g.
  • The formula for weight is:
    • W=m⋅g
      • where m is the mass of the object and g is the acceleration due to gravity.
  • The SI unit of weight is the newton (N), as it is a force.
  • Weight is directly proportional to mass, but mass remains constant everywhere, while weight varies with location (e.g., on different planets).

Effect of Air Resistance:

  • Air resistance affects the rate at which objects fall. For example, a paper and a stone dropped simultaneously will fall at different rates due to air resistance. However, in a vacuum (no air), both objects would fall at the same rate.
  1. Weight and Mass Basics
    • Weight is the force exerted by gravity on an object.
    • The moon’s gravitational pull is weaker than Earth’s because the moon’s mass is smaller.
    • An object’s mass stays constant, but its weight changes based on gravitational force.
  2. Weight on the Moon Formula
    • Using the universal law of gravitation, the weight on the moon, WmW_mWm​, is given by:
      • Wm​= G.Mm.m/R2m​
        • where G is the gravitational constant, Mm​ is the moon’s mass, Rm​ is the moon’s radius, and m is the object’s mass.
  3. Comparison with Earth’s Weight
    • Weight on Earth (WeW_eWe​) is:
      • We​= G.M.m/R
        • Using values for Earth and the Moon, the ratio of weights is approximately: Wm​= 1/6  ​We​
        • An object weighs about 1/6th as much on the moon as it does on Earth.

Thrust and Pressure

  1. Thrust
    • Thrust is the perpendicular force applied to a surface.
  2. Pressure
    • Pressure is defined as force per unit area:
      • Pressure=Thrust/Area​
      • SI unit: Pascal (Pa).
  3. Practical Applications
    • Smaller areas lead to higher pressure, explaining why sharp tools (e.g., knives) cut easily.
    • Wider areas (e.g., camel feet, tank treads) reduce pressure, helping to prevent sinking into soft ground.

Pressure in Fluids and Buoyancy

  1. Fluids and Pressure
    • Fluids (liquids and gases) exert pressure in all directions.
    • Pressure in fluids increases with depth due to the weight of the fluid above.
  2. Buoyancy
    • When an object is immersed in a fluid, it experiences an upward force called buoyant force.
    • This force depends on the density of the fluid.
  3. Why Objects Float or Sink
    • Float: If an object’s density is less than the fluid’s density, the buoyant force exceeds its weight.
    • Sink: If an object’s density is greater, its weight exceeds the buoyant force.

Archimedes’ Principle

  1. Statement
    • When an object is fully or partially submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced.
  2. Applications
    • Used in designing ships, submarines, lactometers (for milk purity), and hydrometers (for liquid density).
  3. Density and Buoyancy
    • Objects less dense than water (e.g., cork) float, while denser objects (e.g., iron nails) sink.

Additional Key Points for Competitive Exams

  1. Universal Law of Gravitation
    • The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
  2. Weight vs. Mass
    • Weight varies with gravity; mass remains constant everywhere.
  3. Practical Examples
    • Swimming pool: You feel lighter due to buoyant force.
    • Floating ships: Shape increases displaced water weight, creating enough buoyant force to float.
    • Weighing cotton vs. iron: Cotton may displace more air, reducing its apparent weight slightly.

THESE ALL ARE THE NOTES OF CHAPTER 9 SCIENCE. AND AFTER SOME TIME YOU GET IMPORTANT QUESTIONS HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊