NCERT Solutions for Class 9 Science Chapter 9 Gravitation
NCERT Solutions for Class 9 Science Chapter 9 Gravitation covers the universal law of gravitation, free fall, acceleration due to gravity (g), mass, weight, weight of an object on the Moon, thrust, pressure, Archimedes' principle, buoyancy, and relative density.
Overview of Topics & Subtopics (Click to Jump)
1. Universal Law of Gravitation & Free Fall
Short Note:
• Universal Law of Gravitation: Every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Formula: F = G × (M × m) / d²
- Universal Gravitational Constant (G): G = 6.673 × 10⁻¹¹ N·m²/kg²
• Free Fall: Whenever an object falls towards Earth under the influence of gravitational force alone, it is said to be in free fall.
• Acceleration due to Gravity (g): Acceleration experienced by a freely falling body due to Earth's gravitational pull. Average value near Earth's surface: g = 9.8 m/s².
- Relation between g and G: g = (G × M) / R²
2. Mass, Weight & Weight on the Moon
Short Note:
• Mass (m): Quantity of matter contained in a body. It remains constant everywhere in the universe. SI Unit: kilogram (kg). Scalar quantity.
• Weight (W): Force with which Earth attracts an object towards its center. Formula: W = m × g. SI Unit: Newton (N). Vector quantity, changes with position/gravity.
• Weight of an Object on the Moon: Since the mass and radius of the Moon are smaller than Earth's, the acceleration due to gravity on the Moon is about 1/6th of that on Earth.
- Weight on Moon = (1/6) × Weight on Earth
3. Thrust, Pressure & Archimedes' Principle
Short Note:
• Thrust: Total net force acting perpendicular to a surface. SI Unit: Newton (N).
• Pressure (P): Thrust per unit area. Formula: Pressure = Thrust / Area. SI Unit: Pascal (Pa) or N/m².
- Smaller area produces greater pressure for the same thrust (e.g., sharp nails, thin straps on bags).
• Archimedes' Principle: When a body is immersed fully or partially in a fluid, it experiences an upward force (buoyant force) equal to the weight of the fluid displaced by it.
- Applications: Designing ships, submarines, hydrometers, lactometers.
4. Buoyancy & Relative Density
Short Note:
• Buoyancy: The upward force exerted by a fluid on an object immersed in it is called buoyant force or upthrust.
- An object floats if its density is less than the density of the fluid.
- An object sinks if its density is greater than the density of the fluid.
• Relative Density: Ratio of the density of a substance to the density of water at 4°C.
- Formula: Relative Density = Density of substance / Density of water
- Since it is a ratio of identical quantities, Relative Density has no unit.
Intext Questions - Page Number: 102
F = G × (M × m) / R²Where:
• F: Gravitational force
• G: Universal gravitational constant
• M: Mass of the Earth
• m: Mass of the object
• R: Radius of the Earth
Intext Questions - Page Number: 104
Textbook Chapter End Exercise Questions
• Mass of Earth (M) = 6 × 10²⁴ kg
• Mass of object (m) = 1 kg
• Radius of Earth (R) = 6.4 × 10⁶ m
• F = G × (M × m) / R²
• F = (6.67 × 10⁻¹¹ × 6 × 10²⁴ × 1) / (6.4 × 10⁶)²
• F = (40.02 × 10¹³) / (40.96 × 10¹²)
• F ≈ 9.77 N ≈ 9.8 N
Pressure = Force / Area). A thin string has a very small contact area, which exerts a large amount of pressure on the shoulder, making it painful and difficult to carry the school bag.
• An object floats if its density is less than the density of water (the buoyant force acting upwards is greater than or equal to the weight of the object).
• An object sinks if its density is greater than the density of water (the buoyant force is less than the weight of the object).
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