Difference Between Gravitational Constant (G) and Acceleration Due to Gravity (g)
The gravitational field strength, commonly denoted as "g", represents the force exerted upon every kilogram of mass in the region surrounding a massive body, like a planet or star. This concept is essential in understanding how gravity causes objects to experience acceleration towards the centre of the mass. Whether it’s a falling apple or a distant satellite orbiting earth, the gravitational field defines the extent of gravitational influence at that location.
Meaning and Importance of Gravitational Field Strength (g)
The value of "g" describes the strength of the gravitational force a massive object exerts around itself. It is fundamental for analyzing free fall, planetary motion, orbits, and determining weight. Simply put, "g" quantifies how much force is exerted on each kilogram of mass at a specific point due to gravity.
Formula for Gravitational Field Strength
The gravitational field strength at any point near a spherical mass can be calculated using Newton’s law of universal gravitation.
The formula is:
- g = gravitational field strength (m/s2)
- G = universal gravitational constant
- M = mass of the object creating the field (kg)
- r = distance from the object’s centre (m)
Physical Significance with Example
If you are standing on Earth's surface, the value of "g" you experience is due to Earth's mass and radius. The farther you move from a massive object's centre, the weaker the gravitational field strength becomes. For example, on Earth's surface, the value of "g" is approximately 9.8 m/s2, meaning every kilogram is attracted with a force of 9.8 newtons towards the centre.
Quantitative Application and Problem-Solving Approach
To solve questions involving gravitational field strength:
- Identify the mass (M) generating the field and the distance (r) from its centre.
- Use the formula: g = G × M / r2.
- Substitute known values and calculate.
Key Formula Table
| Formula / Quantity | Expression | Meaning |
|---|---|---|
| Gravitational Field Strength | g = G × M / r2 | Force per unit mass at a distance r |
| Gravitational Force | F = m × g | Force experienced by mass m in field g |
| Universal Law of Gravitation | F = G × (m1 × m2) / r2 | Attractive force between any two bodies |
Understanding "g" with a Practical Example
Suppose you have a mass of 2 kg at a point where "g" is 9.8 m/s2. The gravitational force experienced will be:
Variation and Characteristics of Gravitational Field Strength
The value of "g" is not universal; it depends on the mass of the planet or object, and the distance from its centre. A larger mass or smaller radius increases "g", and vice versa. As you move outward from the surface of a massive body, "g" decreases follows an inverse square law:
Table: Typical Value of "g" at Various Points
| Position | Distance from Centre (m) | g (m/s2) |
|---|---|---|
| Earth Surface | 6.38 × 106 | 9.8 |
| 1000 km Above Surface | 7.38 × 106 | 7.33 |
| 2000 km Above Surface | 8.38 × 106 | 5.68 |
Next Steps for Mastery
Understanding gravitational field strength is crucial for further topics like orbital motion, satellite dynamics, and advanced celestial mechanics. To strengthen your comprehension:
- Read more on gravitational constant and universal law of gravitation.
- Explore variations of gravity in Gravity and Gravity on Earth discussions.
- Apply formulas to real-world examples with Value of G and Relation between G and g resources.
- Practice calculations with typical Physics problems from Gravitation resource pages.
FAQs on Value of G (Universal Gravitational Constant) Explained for Students
1. What is the value of G?
The value of G, the Universal Gravitational Constant, is:
G = 6.67430 × 10-11 N m2 kg-2 (as per NCERT and NTA 2025 Syllabus).
This value is constant throughout the universe and is used in gravitational force calculations.
2. What is the SI unit of the gravitational constant G?
The SI unit of the gravitational constant G is:
Newton metre2 per kilogram2 (N m2 kg-2).
This unit is used in all standard Physics calculations involving G.
3. What is the formula for G?
The value of G appears in the formula for Newton's Law of Universal Gravitation:
F = G × (m1 × m2) / r2
Here:
• F = Gravitational force
• m1 and m2 = masses
• r = distance between masses
• G = gravitational constant (6.67430 × 10-11 N m2 kg-2)
4. Who determined the value of G first?
The value of G was first measured by Sir Henry Cavendish in 1798 using the famous Cavendish torsion balance experiment.
This experiment allowed the first calculation of the universal gravitational constant and estimation of Earth’s mass.
5. Does G change from place to place?
No, the value of G is universal and does not change from place to place.
• G remains constant everywhere in the universe, regardless of location, altitude, or conditions.
• Unlike small 'g', G is unaffected by local factors.
6. What is the difference between G and g?
G (Universal Gravitational Constant) is a universal constant appearing in Newton's formula for gravitational force, with a value of 6.67430 × 10-11 N m2 kg-2.
g (acceleration due to gravity) refers to the acceleration experienced by an object in a gravitational field, with an average value of 9.8 m/s2 on Earth.
Summary:
• G remains constant everywhere; g varies based on location.
• G is used in formulas for universal gravitation; g is used in motion near Earth’s surface.
7. Why is the value of G so small?
The value of G is extremely small because gravitational force is relatively weak compared to other fundamental forces in nature.
• This small value ensures only massive objects like planets and stars exert significant gravitational attraction.
8. What is the dimensional formula of G?
The dimensional formula for the gravitational constant G is:
[M-1 L3 T-2].
This represents its dimensions in terms of mass (M), length (L), and time (T).
9. How is the value of G measured in experiments?
The value of G is measured using sensitive experiments like the Cavendish Torsion Balance:
• Two small spheres attached to a rod are suspended by a fiber.
• Two large masses are placed near the small spheres.
• The gravitational force between them twists the rod.
• The angular displacement is measured and used to calculate G.
Modern methods use lasers and interferometry for higher accuracy.
10. What is the value of G in CGS units?
In CGS (centimeter-gram-second) units, the value of G is:
G = 6.67430 × 10-8 dyne cm2 g-2.
The CGS system is sometimes used in select Physics problems but SI is standard for exams.
11. What are the applications of the gravitational constant G?
The gravitational constant G has several key applications in Physics:
• Calculating gravitational force between any two masses.
• Estimating planet masses and densities.
• Explaining motion of planets, stars, and satellites.
• Used in Physics formulas in astronomy and astrophysics.
Understanding G is essential for NEET, JEE, and board exams.
12. What is the importance of G in Physics numericals?
G is crucial for solving numericals involving gravitational force and potential energy:
• Always use the correct value of G with matching units.
• Substitute values carefully when using Newton’s law.
• Remember: G is constant; do not confuse it with g or weight in calculations.
Precision in G ensures accurate answers in competitive exams.
