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Universal Law of Gravitation: Definition, Formula & Applications
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The chapter Gravitation discusses Newton's law of universal gravitation, gravitational field and potential, escape velocity, orbital motion, Kepler's laws, and geostationary satellites, which are some of the key topics for the JEE Main exams.
Gravitation Revision Notes: Formulas, Concepts & Quick Guide
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FAQs on Gravitation Revision Notes: Formulas, Concepts & Quick Guide
1. What is gravitation?
Gravitation is the universal force of attraction acting between any two objects with mass.
- This force exists everywhere and is responsible for phenomena like falling apples, planet orbits, and Earth's tides.
- According to Newton’s Universal Law of Gravitation, the strength of gravitation depends on the masses and the inverse square of the distance between them.
- Key terms: gravitation, gravity, universal law, mass, force.
2. What is Newton’s law of universal gravitation?
Newton’s law of universal gravitation states that every object attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- The formula: F = G (m1m2) / r2
- F: gravitational force
- G: universal gravitational constant
- m1, m2: masses
- r: distance between centers of masses
- This law applies to all masses everywhere in the universe.
3. How do you derive acceleration due to gravity?
The acceleration due to gravity (g) is derived using Newton’s law of gravitation and the relation between force and acceleration.
Key derivation steps:
1. Equate gravitational force to the weight of an object on Earth:
F = G (Mem) / Re2 and F = mg
2. Setting G (Mem)/Re2 = mg
3. Solving gives:
g = G Me / Re2
Where Me is mass of Earth, Re is Earth's radius.
- Typical value of g at Earth's surface ≈ 9.8 m/s2.
4. What are the 5 examples of gravitation in daily life?
Common examples of gravitation in daily life include:
- Objects falling to the ground (like a ball or apple)
- Planets orbiting the Sun
- The Moon’s revolution around Earth
- Ocean tides produced by the Moon’s gravity
- Satellites remaining in orbit
These examples demonstrate gravitational force acting at different scales, from daily life to cosmic events.
5. What is the difference between gravity and gravitation?
Gravity specifically refers to the force of attraction exerted by Earth (or another planet) on objects near its surface, while gravitation is the universal attractive force acting between any two masses.
Key differences:
- Gravity: Localized (e.g., Earth’s pull on objects)
- Gravitation: Universal interaction between all masses everywhere
- All gravity is gravitation, but not all gravitation is gravity.
6. What is the value of the universal gravitational constant (G)?
The universal gravitational constant (G) has the value:
- G = 6.674 × 10-11 N m2 kg-2
- It is constant throughout the universe.
- G appears in Newton’s law of gravitation and is used in most gravity-related formulas.
7. What is escape velocity and how is it calculated?
Escape velocity is the minimum speed needed for an object to leave Earth’s (or another celestial body's) gravitational field without further propulsion.
- Formula: vesc = √(2gR) or vesc = √(2GM/R)
- g: acceleration due to gravity
- R: radius of the body
- For Earth, escape velocity ≈ 11.2 km/s.
8. Why does gravitational force not depend on the nature of the intervening medium?
Gravitational force acts directly between masses and is not affected by air, vacuum, or any medium in between.
- This is because gravity arises from mass not from electrical or magnetic properties.
- It is a fundamental force and acts equally well in vacuum.
- No known material alters gravitational attraction between bodies.
9. Is the value of 'g' constant everywhere on Earth?
The value of acceleration due to gravity (g) is not perfectly constant on Earth.
- g decreases with altitude (height), increases slightly at poles, and is lower at the equator.
- g ≈ 9.8 m/s2 at surface, but varies due to Earth's shape, rotation, and density.
- Exam questions often test on factors affecting g.
10. Why do astronauts appear to float in space if gravity is universal?
Astronauts in orbit float because they are in a state of free fall around Earth.
- Gravity still acts on them, but they are constantly falling towards Earth while moving forward.
- This creates a sensation of weightlessness even though gravity is still present.
- It is due to orbital motion, not absence of gravity.
11. What are the basics of gravitation?
The basics of gravitation include its definition, laws, and effects.
- It is attractive, acts between masses, and follows inverse square law.
- Governed by Newton’s universal law.
- Key equations: F = G (m1m2)/r2; g = GM/R2
- Affects planetary motion, tides, free fall, and satellites.
12. Can gravity be zero anywhere in the universe?
Gravity can never be exactly zero anywhere in the universe because every mass exerts a gravitational pull.
- However, gravitational force can be extremely weak in deep space far from all masses.
- Sometimes, forces from different directions can cancel out at certain points (called null points), but gravity itself persists at some level everywhere.
