Introduction to Gravitation for RRB Exams
Gravitation is one of the most fundamental forces in nature, and for any aspirant appearing for the Railway Recruitment Board (RRB) exams like NTPC, Group D, or Technician, it is a non-negotiable topic in the General Science section. From the motion of planets around the sun to why an apple falls to the ground, everything is governed by gravity. In this guide, we will break down the complex concepts of Newton’s Law of Gravitation, the variation of 'g', and Kepler's laws into easy-to-understand segments designed specifically for competitive exam success.
Topic Weightage and Importance
In the General Science (Physics) syllabus of RRB exams, Gravitation typically holds a weightage of 1 to 2 questions per set. For RRB Group D and Technician (Grade I & III) exams, which have a dedicated section for Science, this topic becomes even more critical. You can expect questions ranging from numerical problems on the value of 'g' to conceptual questions about weight on different planets or the properties of satellites. Mastering this topic ensures you don't lose easy marks in the Physics section.
Key Concepts and Formulas
1. Newton’s Universal Law of Gravitation
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 them.
Formula: F = G (m1 × m2) / r²
- F: Gravitational Force
- G: Universal Gravitational Constant (value = 6.674 × 10⁻¹¹ N⋅m²/kg²)
- m1, m2: Masses of the two objects
- r: Distance between the centers of the two masses
2. Acceleration Due to Gravity (g)
The acceleration produced in a body due to the earth's gravitational pull is called acceleration due to gravity. Its average value on Earth is 9.8 m/s².
Relation between G and g: g = GM / R² (where M is mass of Earth and R is its radius).
3. Variation in the value of 'g'
The value of 'g' is not constant everywhere:
- Altitude: 'g' decreases as we go higher from the Earth's surface.
- Depth: 'g' decreases as we go deeper into the Earth. At the center of the Earth, g = 0.
- Shape of Earth: Earth is not a perfect sphere. 'g' is maximum at the Poles and minimum at the Equator.
4. Mass vs. Weight
| Feature | Mass | Weight |
|---|---|---|
| Definition | Amount of matter in a body. | Force of gravity acting on a body. |
| SI Unit | Kilogram (kg) | Newton (N) |
| Nature | Constant everywhere. | Changes with gravity (W = mg). |
5. Escape Velocity and Orbital Velocity
- Escape Velocity (Ve): The minimum velocity required for an object to escape Earth's gravity. For Earth, it is 11.2 km/s.
- Orbital Velocity (Vo): The velocity required for a satellite to stay in its orbit. For a satellite near Earth, it is approx. 7.9 km/s.
6. Kepler’s Laws of Planetary Motion
- Law of Orbits: All planets move in elliptical orbits with the Sun at one focus.
- Law of Areas: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
- Law of Periods: The square of the time period of a planet (T) is proportional to the cube of the semi-major axis of its orbit (R). (T² ∝ R³).
Solved Examples (Step-by-Step)
Example 1: An object has a mass of 60 kg on Earth. What will be its weight on the Moon? (Gravity on Moon is 1/6th of Earth's gravity).
Solution:
1. Mass remains constant, so mass on Moon = 60 kg.
2. Acceleration due to gravity on Earth (g) = 9.8 m/s².
3. Weight on Earth = m × g = 60 × 9.8 = 588 N.
4. Weight on Moon = (1/6) × Weight on Earth = 588 / 6 = 98 N.
Example 2: If the distance between two objects is doubled, what happens to the gravitational force between them?
Solution:
1. Force F = G(m1m2)/r².
2. If new distance R' = 2r, then new Force F' = G(m1m2)/(2r)².
3. F' = G(m1m2)/4r² = F/4.
4. The force becomes one-fourth of the original force.
Example 3: At what point is the value of acceleration due to gravity (g) zero?
Solution: The value of 'g' decreases as we move toward the center of the earth. At the exact center of the Earth, the gravitational pull from all directions cancels out, making g = 0.
Common Mistakes to Avoid
- Confusing 'G' and 'g': Remember that 'G' is the Universal Constant (same everywhere in the universe), while 'g' is acceleration due to gravity (changes based on location).
- Mass vs. Weight: Students often use 'kg' for weight in calculations. Weight is a force and must be in Newtons (N).
- Radius units: When solving numericals, always ensure distance is in meters (m) and mass is in kilograms (kg) to match the SI units of G.
- Square of distance: In the gravitation formula, many forget to square the distance (r²), leading to incorrect results.
Practice Questions with Solutions
1. What is the value of the Universal Gravitational Constant (G)?
2. If a person moves from the Equator to the North Pole, what happens to their weight?
3. What is the escape velocity of an object from the surface of the Moon?
4. Which law states that the square of the time period of a planet is proportional to the cube of its distance from the sun?
5. What is the weight of a 10 kg body at the center of the Earth?
Solutions:
- 6.674 × 10⁻¹¹ N⋅m²/kg².
- The weight increases because the value of 'g' is higher at the poles.
- Approximately 2.38 km/s (Much lower than Earth's 11.2 km/s).
- Kepler's Third Law (Law of Periods).
- Zero, because 'g' is zero at the center of the Earth.
Frequently Asked Questions (FAQs)
Q1: Does gravity exist in a vacuum?
A1: Yes, gravity exists in a vacuum. A vacuum only means the absence of air/matter, but gravitational fields can still exist there (e.g., the Moon orbits Earth in the vacuum of space).
Q2: Why do astronauts feel weightless in space?
A2: They feel weightless because they are in a state of continuous free fall while orbiting the Earth, not because there is no gravity.
Q3: What is the relation between mass of Earth and gravity?
A3: Gravity is directly proportional to the mass of the planet. If Earth's mass were doubled (keeping radius same), 'g' would also double.
Conclusion and Final Tips
Gravitation is a conceptual yet scoring topic. To excel in RRB NTPC, Group D, or Technician exams, focus on the inverse square law and the variations of 'g'. Practice converting mass to weight and remember the standard values of G, g, and escape velocity. Keep your concepts clear, and you will find these questions to be some of the fastest to solve during the actual exam. Stay consistent in your preparation, and good luck!
