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What is Newton’s Universal Law of Gravitation?
Gravitation is the fundamental force that causes masses to attract each other in the universe. It keeps planets in their orbits and objects firmly on Earth's surface, making it a core topic for JEE Main Physics.
Understanding gravitation helps explain why apples fall, why satellites revolve, and how tides are formed. The importance of this force extends across mechanics, astronomy, and daily life.
Definition and Law of Gravitation
In simple terms, gravitation is the universal force of attraction between any two bodies with mass. For JEE, the central principle is Newton’s Law of Universal Gravitation.
- Every two point masses attract each other.
- The force is directly proportional to the product of their masses.
- The force is inversely proportional to the square of the distance between them.
- This force acts along the line joining their centers.
The mathematical form is: F = G (m1m2/r2). Here, F is gravitational force, G is the gravitational constant, m1, m2 are the masses, and r is the distance between centers.
You can deepen your understanding by reading the derivation in the page on universal law of gravitation derivation. The Newton's laws of motion page provides more context about forces and motion.
Derivation and Key Formulae in Gravitation
The derivation of the gravitation formula is a frequent JEE exam task. It starts with Newton’s insight and proceeds stepwise:
- Two masses, m1 and m2, separated by distance r.
- The force is proportional to m1m2.
- It is inversely proportional to r2.
- F = G (m1m2/r2) combines both ideas.
- G (gravitational constant) is always the same: 6.67 × 10-11 N·m2/kg2.
The gravitational potential energy between two masses is given by U = -G(m1m2/r). To practice such formulae, refer to gravitation practice paper and mock test on gravitation.
| Quantity | Symbol | SI Unit |
|---|---|---|
| Gravitational Force | F | newton (N) |
| Gravitational Constant | G | N·m2/kg2 |
| Acceleration due to Gravity | g | m/s2 |
Explore the impact of acceleration due to gravity and its variations at different places for strong conceptual preparation.
Gravitational Field, Potential, and Weight
A gravitational field exists around every mass. The field strength at a point is the force experienced per unit mass. g = GM/r2 near a mass M. Gravitational potential at a distance r is V = -GM/r.
The weight of a body is the force of gravity it experiences: W = mg. Learn differences between mass and weight and review motion under gravity for JEE applications.
Real-life Examples and JEE Applications of Gravitation
Gravitation explains why planets orbit the Sun, why satellites move in fixed paths, and why objects fall to the ground. These ideas are tested routinely in the exam.
- Satellites remain in orbit due to balance of gravitational force and their velocity.
- Weightlessness in space comes from free fall under gravity alone.
- Tides arise due to Moon’s gravitational pull on Earth’s waters.
- Escape velocity calculation is a classic JEE question.
- Planetary orbits explained by Newton’s law and Kepler’s laws.
For in-depth orbits, use the guide to motion of satellites. Test yourself with the gravitation mock test 1.
A vital application is finding acceleration due to gravity at different locations. Remember, g differs with altitude, latitude, and Earth’s shape. Use effective gravity notes for related numericals. This is a frequent exam area.
Common Pitfalls and Mistakes in Gravitation
- Confusing gravitation (the general force) with gravity (Earth’s attraction).
- Forgetting that G is a universal constant while g varies from place to place.
- Neglecting negative signs in potential energy expressions.
- Misapplying the inverse-square law for forces between extended rather than point masses.
- Missing SI units in final answers, especially for G and F.
Review law of motion important questions and types of forces in physics to sharpen your skills on gravitation problems and avoid exam errors.
Worked Example: Universal Gravitation
Two objects, each 2 kg, are 1 metre apart. Find the force between them.
- F = G (m1m2/r2)
- G = 6.67 × 10-11 N·m2/kg2
- m1 = m2 = 2 kg; r = 1 m
- F = 6.67 × 10-11 × 2 × 2 ÷ 12
- F = 2.67 × 10-10 N
This result, though small, illustrates Newton’s law in daily objects. For advanced problems and JEE strategy, visit the gravitation important questions page.
For full coverage, see gravitation revision notes and kinetic theory of gases for links between microscopic and cosmic forces.
The gravitation topic is guided by well-experienced Vedantu Physics experts, aligned with latest JEE Main syllabus. Mastering these ideas links you to astronomy, engineering, and emerging sciences.
Gravitation: Concepts, Laws, and Important Formulas
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FAQs on Gravitation: Concepts, Laws, and Important Formulas
1. What is the simple definition of gravitation?
Gravitation is the force by which all objects with mass attract each other.
- It keeps planets in orbit around the Sun.
- It causes objects to fall towards the Earth.
- Gravitation acts between any two masses, no matter how far apart.
- This phenomenon is central in both physics and everyday life.
2. What are the three laws of gravitation?
Newton’s three laws of gravitation describe how gravity works between objects.
1. Every mass attracts every other mass.
2. The force of attraction is directly proportional to the product of their masses.
3. The force is inversely proportional to the square of the distance between them.
The mathematical form is: F = G (m1m2/r2)
3. What is the value of g?
The standard value of g (acceleration due to gravity) on Earth's surface is 9.8 m/s2.
- This means every second, an object’s speed increases by 9.8 meters per second when falling freely.
- The value can vary slightly depending on location due to Earth’s shape and density.
4. What is an example of gravitation?
A common example of gravitation is an apple falling from a tree to the ground.
- The Earth's gravitational force pulls the apple down.
- Other examples include the Moon orbiting the Earth and planets revolving around the Sun.
5. What is the gravitation formula?
Newton's law of universal gravitation formula is:
F = G (m1m2/r2)
- F = Gravitational force
- G = Universal gravitational constant (6.674 × 10-11 N·m2/kg2)
- m1 and m2 = Masses of two objects
- r = Distance between the centers of the two masses
6. What is gravitational potential energy?
Gravitational potential energy is the energy stored in an object due to its position in a gravitational field.
- For objects near Earth's surface, it is calculated as U = mgh, where m is mass, g is acceleration due to gravity (9.8 m/s2), and h is the height above ground.
7. What is gravitational force?
The gravitational force is the attraction between two masses due to gravity.
- It is always attractive in nature.
- Acts along the line joining the centers of the two objects.
- Its magnitude depends on the product of the masses and inversely on the square of the distance between them.
8. What is the gravitational constant?
The gravitational constant (G) is a fundamental constant used in the universal law of gravitation.
- Its value is 6.674 × 10-11 N·m2/kg2.
- It determines the strength of gravitational force between two objects.
9. What are gravitational waves?
Gravitational waves are ripples in spacetime caused by the acceleration of massive objects.
- They were predicted by Einstein's theory of general relativity.
- Examples include waves produced by merging black holes or neutron stars.
- Detected for the first time in 2015 by LIGO.
10. What is gravitational lensing?
Gravitational lensing occurs when light from a distant object is bent around a massive body due to gravity.
- This effect acts like a natural lens, magnifying or distorting the image.
- Used by astronomers to study galaxies, dark matter, and the universe’s structure.
11. What is meant by gravitational pull?
Gravitational pull refers to the force with which a massive object, like Earth, attracts other objects towards its center.
- Responsible for keeping us grounded.
- The strength of the pull depends on mass and distance.
12. What is the formula for gravitational potential energy?
The formula for gravitational potential energy (U) near Earth's surface is:
U = mgh
- m = mass of the object
- g = acceleration due to gravity (9.8 m/s2)
- h = height above ground
