Gravitation: A Guide for CBSE Class 9 Science

Have you ever wondered why a ball thrown up always comes back down? Or how the Moon circles the Earth without flying off into space? The answer to these mysteries is a fundamental force of nature: Gravitation. It's the invisible string that keeps everything together, from you standing on the ground to planets orbiting the Sun.

In this chapter on Gravitation for Class 9 Science, we will explore the brilliant ideas of Sir Isaac Newton. You will master the Universal Law of Gravitation, which describes how any two objects with mass attract each other. We will also dive into concepts like free fall, acceleration due to gravity (g), and the crucial difference between mass and weight. By the end, you'll be able to calculate gravitational forces and understand the beautiful mechanics that govern our universe. Let's begin this exciting journey!

The Universal Law of Gravitation

The foundation of this chapter is Newton's Universal Law of Gravitation. It states that 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.

This might sound complex, but let's break it down.

Directly proportional to the product of their masses (m₁ × m₂): This means if you increase the mass of either object, the gravitational force between them increases.
Inversely proportional to the square of the distance (1/d²): This is the 'inverse-square law'. It means that as you double the distance between two objects, the force becomes four times weaker (2² = 4). If you triple the distance, the force becomes nine times weaker (3² = 9).

Mathematically, we write this law as:

**F = G (m₁ m₂) / d²**

Where:

F is the gravitational force between the objects.
G is the Universal Gravitational Constant.
m₁ and m₂ are the masses of the two objects.
d is the distance between the centers of the two objects.

Key Terms in Gravitation

Universal Gravitational Constant (G): The constant of proportionality in Newton's law of gravitation. Its value is experimentally found to be 6.673 × 10⁻¹¹ N m²/kg². It is 'universal' because its value is the same everywhere in the universe.
Free Fall: The motion of an object where gravity is the only force acting upon it. In an ideal scenario (no air resistance), any object in free fall accelerates downwards at the same rate, regardless of its mass.
Acceleration due to Gravity (g): The acceleration gained by an object due to Earth's gravitational force. On the surface of the Earth, its average value is approximately 9.8 m/s². This value changes slightly with altitude and position on Earth.
Weight: The force with which an object is attracted towards the center of a celestial body (like Earth). It is calculated as the product of the object's mass and the local acceleration due to gravity (W = m × g). Its unit is the Newton (N).

Worked Example: Calculating Gravitational Force

Problem: Calculate the force of gravitation between the Earth and a 1 kg object on its surface. (Given: Mass of Earth, M = 6 × 10²⁴ kg, Radius of Earth, R = 6.4 × 10⁶ m, and G = 6.67 × 10⁻¹¹ N m²/kg²) Solution: Step 1: Identify the known values. Mass of Earth (m₁) = M = 6 × 10²⁴ kg Mass of the object (m₂) = 1 kg Distance between centers (d) = Radius of Earth, R = 6.4 × 10⁶ m Universal Gravitational Constant (G) = 6.67 × 10⁻¹¹ N m²/kg² Step 2: Write down the Universal Law of Gravitation formula. F = G (m₁ m₂) / d² Step 3: Substitute the known values into the formula. F = (6.67 × 10⁻¹¹) ( (6 × 10²⁴) 1 ) / (6.4 × 10⁶)² Step 4: Simplify the equation. F = (6.67 × 6 × 10⁻¹¹⁺²⁴) / (6.4 × 6.4 × 10⁶*²) F = (40.02 × 10¹³) / (40.96 × 10¹²) Step 5: Perform the final calculation. F = (40.02 / 40.96) × 10¹³⁻¹² F ≈ 0.977 × 10¹ F ≈ 9.77 N Final Answer: The gravitational force between the Earth and a 1 kg object on its surface is approximately 9.8 N. This force is what we call the weight of the object.

Exam Tip: Distinguishing Between 'G' and 'g'

A very common point of confusion for students is the difference between the Universal Gravitational Constant (G) and the acceleration due to gravity (g). It's crucial to know the distinction for your exams.

Remember: G is a universal property that links mass and distance to force. g is the result of that force from a large body like a planet acting on a smaller object near its surface.

Practice Questions with Solutions

Q: What happens to the gravitational force between two objects if the distance between them is doubled? A: Step 1: Recall the Universal Law of Gravitation, F = G (m₁m₂)/d². This shows that force (F) is inversely proportional to the square of the distance (d²). Step 2: Let the new distance be d' = 2d. The new force F' will be F' = G (m₁m₂)/(2d)² = G (m₁m₂)/(4d²). Step 3: Compare the new force with the original force. F' = (1/4) [G * (m₁m₂)/d²] = F/4. Final answer: If the distance between the two objects is doubled, the gravitational force becomes one-fourth (1/4) of its original value.
Q: An object has a mass of 20 kg. What is its weight on Earth? (Take g = 9.8 m/s²) A: Step 1: Identify the given values: mass (m) = 20 kg and acceleration due to gravity (g) = 9.8 m/s². Step 2: Recall the formula for weight: Weight (W) = mass (m) × acceleration due to gravity (g). Step 3: Substitute the values into the formula: W = 20 kg × 9.8 m/s². Step 4: Calculate the product: W = 196 N. Final answer: The weight of the object on Earth is 196 Newtons.
Q: An astronaut's mass on Earth is 72 kg. The acceleration due to gravity on the Moon is about 1/6th of that on Earth. What is the astronaut's (a) mass and (b) weight on the Moon? A: Step 1: (a) Understand the concept of mass. Mass is the amount of matter in an object and it remains constant regardless of location. Step 2: Therefore, the astronaut's mass on the Moon is the same as on Earth. Mass on Moon = 72 kg. Step 3: (b) Calculate the astronaut's weight on the Moon. First, find the acceleration due to gravity on the Moon (g_moon). g_moon = (1/6) g_earth = (1/6) 9.8 m/s² ≈ 1.63 m/s². Step 4: Use the weight formula W = m × g_moon. W_moon = 72 kg × 1.63 m/s² ≈ 117.36 N. Final answer: The astronaut's mass on the Moon is 72 kg, and their weight is approximately 117.4 N.
Q: Calculate the value of acceleration due to gravity 'g' on the surface of the Earth. (Use the values from the worked example: M = 6 × 10²⁴ kg, R = 6.4 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m²/kg²) A: Step 1: Recall the relationship between g and G: g = G M / R². Step 2: Substitute the given values into the formula: g = (6.67 × 10⁻¹¹) (6 × 10²⁴) / (6.4 × 10⁶)². Step 3: This calculation is identical to the one for force on a 1 kg object in our worked example. g = (40.02 × 10¹³) / (40.96 × 10¹²). Step 4: Perform the final calculation: g ≈ 0.977 × 10¹ ≈ 9.77 m/s². Final answer: The calculated value for acceleration due to gravity 'g' on the Earth's surface is approximately 9.8 m/s².

Frequently Asked Questions

What is the difference between mass and weight?

Mass is the amount of matter in an object and is constant everywhere, measured in kilograms (kg). Weight is the gravitational force acting on that mass (W = mg) and changes depending on the strength of gravity, measured in Newtons (N).

Why don't we feel the gravitational pull from everyday objects like a table or a chair?

The gravitational force exists, but it is extremely weak. The masses of everyday objects are very small, so the resulting force is negligible and easily overcome by other forces like friction.

If the Earth pulls an apple down, does the apple also pull the Earth up?

Yes, absolutely! According to Newton's Third Law, the force is equal and opposite. However, because the Earth's mass is gigantic compared to the apple's, the force from the apple produces an immeasurably small acceleration on the Earth.

Is the value of 'g' constant everywhere on Earth?

No, it is not. The value of 'g' is slightly greater at the poles and lesser at the equator because Earth is not a perfect sphere. It also decreases as you go to higher altitudes or deep into the Earth.