How is Gravitational Constant (G) Used in Physics Problems?
The gravitational constant is an important quantity in Physics that helps describe the attractive force between any two objects with mass. It is a fundamental constant denoted by the symbol G and appears directly in the formula for gravitational attraction. This constant helps students, teachers, and parents understand how gravity governs interactions, from small laboratory objects to planets and stars.
Definition and Concept of Gravitational Constant
The gravitational constant, represented as G, is a physical constant used to calculate the force of gravity between two objects. The mathematical formula defining this relationship is:
F = G × (m₁ × m₂) / r²
Here,
- F is the gravitational force between the objects,
- m₁ and m₂ are their masses,
- r is the distance between the centers of the two masses,
- G is the gravitational constant.
G quantifies how strongly two masses attract each other. Its value remains constant for any pair of objects, regardless of their size or the distance that separates them.
Numerical Value and Units of G
The official value of the gravitational constant is:
G = 6.6743 × 10-11 m³·kg-1·s-2
This value tells us that the force of gravity is very weak unless large masses are involved or the distance between objects is extremely small. The units break down as:
- m³: meter cubed (volume measure)
- kg: kilogram (mass measure)
- s: second (time measure)
The unit can also be expressed as N·m²/kg² (Newton meter squared per kilogram squared) in SI units.
| Parameter | Value | Unit | Use |
|---|---|---|---|
| Gravitational Constant (G) | 6.6743 × 10-11 | m³·kg-1·s-2 | SI System (Physics and Astronomy) |
Application and Example
Let us see how to use the gravitational constant in a practical formula:
Suppose you wish to calculate the gravitational force between two objects, each of mass 5 kg, separated by a distance of 1 meter. Using the formula:
- m₁ = 5 kg
- m₂ = 5 kg
- r = 1 m
- G = 6.6743 × 10-11 m³·kg-1·s-2
Substituting these values:
F = 6.6743 × 10-11 × (5 × 5) / (1)²
F = 6.6743 × 10-11 × 25
F = 1.668575 × 10-9 N
So, the gravitational force is extremely small (about 1.67 × 10-9 Newtons).
Step-by-Step Approach to Solving Gravitational Force Problems
- Write down the values of m₁, m₂, and r from the question.
- Remember or refer to the value of G as given in the SI system.
- Substitute all values into the formula F = G × (m₁ × m₂) / r².
- Carry out the calculation step-by-step: first multiply the masses, then divide by the square of the distance.
- Multiply the result by G and write the answer with proper units (N or Newton).
Key Points to Remember
- G is a constant for all situations in classical physics.
- The gravitational force increases if the masses increase or the distance between them decreases.
- The gravitational constant is not affected by the type of material or where in the universe the measurement is made.
- It is fundamental in calculating forces between planets, satellites, and other astronomical objects.
| Formula | Terms | Description |
|---|---|---|
| F = G × (m₁ × m₂) / r² |
F: Force between masses
m₁, m₂: Masses r: Distance G: Gravitational Constant |
Main formula for calculating gravitational force |
Practice Questions
- Calculate the gravitational force between two objects with masses of 2 kg and 3 kg kept 4 meters apart.
- If the distance between two 10 kg objects is doubled, by what factor does the gravitational force change?
Explore More on Vedantu
- Gravitation - Complete Topic Summary
- Gravitational Constant and Universal Law of Gravitation
- Value of g (Acceleration Due to Gravity)
- Gravity - Concept and Applications
- Gravity on Earth
- Universal Law of Gravitation
Next Steps for Learners
- Revise the formula and units for the gravitational constant.
- Practice at least five numerical questions using the formula F = G × (m₁ × m₂) / r².
- Explore real-life examples, such as the force between the Earth and the Moon.
- Use the properties of G to understand advanced topics in gravity and astronomy.
- Refer to more Vedantu resources for in-depth explanations and additional practice.
Understanding the value and application of the gravitational constant helps in solving fundamental questions in Physics. For further revision and deeper conceptual clarity, students can utilize the practice questions and resources linked above. Mastery of this concept lays the foundation for Physics topics such as Gravitation, Gravity, and many more.
FAQs on Gravitational Constant (G): Value, Units, Formula & Explanation
1. What is the value of the gravitational constant (G) in SI units?
The value of the gravitational constant (G) in SI units is:
G = 6.674 × 10-11 N·m2/kg2
This value is recommended by CODATA and is used in all major Physics exams and textbooks.
2. What does the gravitational constant G represent?
The gravitational constant G is a universal constant that quantifies the strength of the gravitational force between two bodies.
Key points about G:
- It appears in Newton’s law of universal gravitation.
- It remains the same everywhere in the universe.
- Represents the force between two 1-kg masses kept 1 meter apart.
3. What is the formula for calculating gravitational force?
The gravitational force between two masses is given by:
F = G · (m1m2 / r2)
• F = gravitational force
• G = gravitational constant
• m1 and m2 = masses
• r = distance between object centers
4. What are the units of the gravitational constant in CGS and English (FPS) systems?
The units of G in different systems are:
- CGS: 6.674 × 10-8 dyne·cm2/g2
- English (FPS): 1.071 × 10-9 ft3/lb·s2
5. Is the value of G the same everywhere in the universe?
Yes, the value of the gravitational constant (G) is universal and remains the same everywhere in the universe. G does not depend on location, planet, altitude, or time.
6. What is the difference between G and g?
G is the universal gravitational constant (6.674 × 10-11 N·m2/kg2), while g is the acceleration due to gravity (9.8 m/s2 on Earth).
• G is constant everywhere
• g varies based on location and planet
7. How is the gravitational constant (G) determined experimentally?
The value of G was first measured using the Cavendish experiment (1798), which used a torsion balance to measure the tiny force between known masses.
This was the first direct laboratory measurement of the gravitational constant.
8. Why is G called a "universal" constant?
G is called universal because its value is the same everywhere in the universe, for all objects and at all times. It applies to all massive bodies equally, regardless of their composition or location.
9. What is the importance of the gravitational constant in Physics?
The gravitational constant G determines the strength of gravity in Newton’s law, allowing calculation of:
- Gravitational force between objects
- Orbital mechanics of planets and satellites
- Variation of g with altitude and planetary radius
10. Does the value of G change on the Moon or other planets?
No, the value of G does not change on the Moon, Earth, or any other planet.
Only g (acceleration due to gravity) varies based on the mass and radius of the celestial body, but G remains constant everywhere.
11. What is the dimensional formula of the gravitational constant G?
The dimensional formula of G is:
[M-1 L3 T-2]
Where M = mass, L = length, T = time.
12. How can I remember the value and units of G for exams?
Use this tip:
• G is a small number close to 6.67 × 10-11 N·m2/kg2
• The unit combines Newton, meter squared, and kilogram squared
• Practice writing the value before exams to improve recall
