Chapter 10: Gravitation - Class 9 Science
1. Gravitational Force of Earth
→ If we release a small stone without pushing it from a height, it accelerates towards Earth.
→ The stone is accelerated towards Earth, indicating some force is acting on it. The force pulling objects towards the center of the Earth is known as gravitational force of the Earth.
→ The stone also attracts Earth. This means every object in the universe attracts every other object.
2. Newton’s Universal Law of Gravitation
→ Sir Isaac Newton in 1687 proposed a law about the force of attraction between two objects in the universe, known as Newton’s law of gravitation.
According to Universal Law of Gravitation
→ Every mass in this universe attracts every other mass with a force directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.
→ Let masses (M) and (m) of two objects be distance (d) apart. Then the force of attraction (F) between them is:
- → F ∝ M × m
- → F ∝ 1/d²
- → F ∝ Mm/d²
- → F = (GMm)/d²
→ Where G is a constant known as the Gravitational constant. The value of G = 6.67 × 10⁻¹¹ Nm²/kg².
→ If the unit of F is in Newton, m is in kg, and d is in meters, then the unit of G is Nm²/kg².
3. Relation between Newton’s Third Law of Motion and Newton’s Law of Gravitation
→ According to Newton’s third law of motion, “Every object exerts equal and opposite force on another object but in the opposite direction.”
→ According to Newton’s law of gravitation, “Every mass in the universe attracts every other mass.”
→ In the case of a freely falling stone and Earth, the stone is attracted towards Earth, meaning Earth attracts the stone.
→ According to Newton’s third law of motion, the stone should also attract Earth. This is true; the stone attracts Earth with the same force, but due to the stone’s very small mass, its acceleration is negligible.
4. Importance of Universal Law of Gravitation
- → The force that binds us to the Earth.
- → The motion of the Moon around the Earth.
- → The motion of the Earth around the Sun.
- → The tides due to the Moon and the Sun.
5. Free Fall of an Object and Acceleration (g)
→ When an object is thrown upward, it reaches a certain height and then starts falling towards Earth due to Earth’s gravitational force.
→ This fall under the influence of Earth is called ‘free fall of an object’.
→ During free fall, the direction does not change, but velocity continuously changes, which is called acceleration due to gravity. It is denoted by ‘g’.
→ The unit of ‘g’ is the same as acceleration, m/s².
6. Gravitational Acceleration and Its Value at the Surface of Earth
→ The uniform acceleration produced in a freely falling object due to Earth’s gravitational force is called acceleration due to gravity.
→ It is represented by ‘g’ and always acts towards the center of the Earth.
→ The value of ‘g’ on the surface of the Earth is given by:
- → F = (GMem)/R² .... (i)
- → where, Me = Mass of Earth
- → m = Mass of an object
- → R = Radius of Earth
- → If acceleration due to gravity is ‘g’, then F = m × g .... (ii)
7. Relationship and Difference between ‘G’ and ‘g’
- → G = Gravitational constant
- → g = Acceleration due to gravity
- → g = GM/R²
→ Difference between G (Gravitational constant) and g (Acceleration due to gravity):
| Gravitational Constant (G) | Gravitational Acceleration (g) |
|---|---|
| Its value is 6.67 × 10⁻¹¹ Nm²/kg². | Its value is 9.8 m/s². |
| Its value remains constant everywhere. | Its value varies at various places. |
| Its unit is Nm²/kg². | Its unit is m/s². |
| It is a scalar quantity. | It is a vector quantity. |
8. Example: Falling Stones
→ If two stones of 150 gm and 500 gm are dropped from a height, which stone will reach the surface of the Earth first and why?
→ Galileo first demonstrated that the acceleration of an object falling freely towards Earth does not depend on the mass of the object.
→ This can be verified by Newton’s law of gravitation. Let an object of mass m fall from a distance of R from the center of Earth. The gravitational force F = (GMem)/R². The force acting on the stone is F = m × a. Thus, acceleration a = GMe/R².
→ Acceleration is independent of the mass of the stone.
→ Therefore, both stones will reach the ground at the same time if dropped from the same height.
9. Thrust and Pressure
→ When force is applied on an object, it exerts a force on the surface in contact. This force is called thrust.
→ The thrust acting per unit area is called pressure.
→ Pressure (P) = Thrust (F) / Area (A)
10. Buoyancy and Archimedes’ Principle
→ An object placed in a fluid (liquid or gas) experiences an upward force, known as the buoyant force, which opposes the weight of the object.
→ Archimedes’ principle states: "When an object is immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced by the object."
11. Relative Density
→ Relative density is the ratio of the density of a substance to the density of a reference substance (usually water).
→ It is a dimensionless quantity.
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