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Gravity is the force by which a planet or other body draws objects toward its center. It is often referred to as “a force exerted by the Earth to pull objects towards it”. However, gravity is not limited to the Earth and the objects close to it.
What is the Universal Law of Gravitation?
According to the universal law of gravitation, every object in the universe attracts every other object with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The gravitational force formula can be written by introducing a proportionality constant ‘G’ as follows:
The proportionality constant G is called the universal gravitational constant. The universally accepted gravitational constant value is as follows:
The formula of Acceleration due to Gravity (g):
Let us try to find the value of acceleration due to gravity. For this, we will consider the case of a freely falling object. Consider a stone of mass ‘m’ falling freely under the influence of gravity only.
According, to Newton’s second law the force acting on the stone will be:
F = m x g ……… (1)
Now, if we consider the mass of the Earth to be ‘M’ and the distance between the stone of mass ‘m’ and the Earth to be ‘d’. As the distance between the center of the stone to the earth’s surface is negligible, we can consider ‘d’ as the radius ‘R’ of the earth. The gravitational force formula is given as,
Dividing both sides by the mass of the object ‘m,’
The values of the universal gravitational constant, the mass of the earth ‘M,’ and the radius of the earth ‘R’ are,
G = 6.673 x 10-11 Nm2 kg-2
M = 6 x 1024 Kg
R = 6.4 x 106 m
On substituting them, we get the value of acceleration due to the gravity on the earth as,
g = 9.8 m/s2
Unit of Acceleration due to Gravity:
The unit of acceleration due to gravity is meters per second squared (m/s2). It represents the rate at which an object accelerates toward the Earth’s surface under the influence of gravity. The value of acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s2.
Solved Examples on Gravity Formula:
Example 1: Calculating the acceleration due to gravity on the surface of a planet
Given:
Mass of the planet (M) = 5.972 × 1024 kg
The radius of the planet (r) = 6.371 × 106 meters
Gravitational constant (G) = 6.67430 × 10-11 N(m/kg)2
To determine the acceleration due to gravity (g) on the planet’s surface, we use the formula:
g = (G x M) / r2
Substituting the values:
g = (6.67430 × 10-11 x 5.972 × 1024 kg) / (6.371 × 106 m)2
g = (6.67430 × 10-11 x 5.972 × 1024 kg) / 4.049 × 1013 m2
g = 9.8227 m/s2
Therefore, the acceleration due to gravity on the surface of the planet is approximately 9.8227 m/s2.
Example 2: Calculating the weight of an object
Given:
Mass of the object (m) = 60 kg
Acceleration due to gravity (g) on Earth = 9.8 m/s2
To find: Weight of the object (W)
Solution:
Weight is calculated using the formula: W = m x g
Substituting the given values:
W = 60 kg x 9.8 m/s2
W = 588 N
Therefore, the weight of the object is 588 Newton.
FAQ’s on Gravity Formula
What is gravity?
Gravity is a fundamental force in nature that attracts objects with mass towards each other. It is responsible for phenomena such as the falling of objects, the motion of planets, and the formation of galaxies.
Who discovered gravity?
The concept of gravity has been understood and observed since ancient times. However, Sir Isaac Newton's work in the 17th century, particularly his law of universal gravitation, provided a mathematical framework for describing and understanding gravity.
What is G in physics?
In physics, G refers to the gravitational constant, also known as the universal gravitational constant. It is denoted by the symbol G and represents the strength of the gravitational force between two objects. The value of the gravitational constant is approximately 6.674 × 10-11 N(m/kg)2 in the International System of Units (SI). It plays a crucial role in the calculation of gravitational forces and is used in various formulas, including Newton's law of universal gravitation. The gravitational constant provides a fundamental constant that helps quantify the force of gravity between objects and is an essential component of gravitational calculations in physics.
How does gravity work?
According to Einstein's general theory of relativity, gravity is the result of the curvature of spacetime caused by mass or energy. Massive objects create a curvature in spacetime, and other objects move along the curves in response, creating the effect we perceive as gravity.
Is gravity the same everywhere in the universe?
Gravity is present throughout the universe, but its strength can vary depending on the masses of the objects involved and the distances between them. Gravity is stronger for objects with larger masses and weaker for objects that are farther apart.
Can gravity be shielded or blocked?
Gravity is a long-range force that cannot be shielded or blocked by any known material or method. It acts on all objects with mass, regardless of barriers or intervening materials.
Does gravity only pull objects down?
No, gravity is an attractive force that acts between any two objects with mass. On Earth, gravity pulls objects towards the center of the planet, giving the perception of downward motion. In space, gravity can cause objects to orbit or attract each other.
Where is gravity maximum on the earth?
Gravity is maximum near the surface at the pole. It is slightly stronger at the poles compared to the equator. This is because the Earth is not a perfect sphere but slightly flattened at the poles due to its rotation. As a result, the distance between an object at the poles and the center of the Earth is slightly shorter than at the equator, leading to a slightly stronger gravitational force.
Does gravity affect light?
Yes, gravity can affect the path of light. According to Einstein's theory of general relativity, gravity can bend the path of light, causing it to follow a curved trajectory when passing close to a massive object.
