Gravitational Force: Gravity, Formula, Examples

According to Newton’s Law of Gravitation, the Gravitational Force is a universal force between all the matter. When you throw a stone or any other object upwards, it falls back on the ground. Have you ever wondered why this happens? This happens because of a force that attracts all the objects towards the Earth. The force attracting an object towards the Earth’s centre or any other planet or moon is called Gravity. In this article, let’s understand what Gravity is and its importance to us.

All bodies on Earth have a weight, or downward force of gravity, proportional to their mass, which is exerted on them by the Earth’s mass. The acceleration that gravity imparts toly falling objects is used to quantify gravity. The acceleration of gravity at the Earth’s surface is roughly 9.8 meters (32 feet) per second.

In this article, we will discuss in detail about what is gravity, gravitational force, laws, formulas, solved examples, etc. Continue reading to know more.

What is Gravity?

While sitting under a tree, Sir Isaac Newton discovered an apple falling from the tree. Then he tried to figure out why the apple fell on the ground instead of going left or right. This made him think that a force is pulling the apple towards the earth. Then he assumed that the force of attraction acting between all objects in the universe and named this a force of gravity or force of gravitation.

Definition: Gravity is the force that attracts a body towards the centre of the earth or any other body which has mass. The force of gravity is a special case of the force of gravitation, where one of the objects has an infinitely large mass as compared to the other body. For example, the force of gravity acting between the earth and the objects on or around its surface.

Gravity is a non-contact force as it does not need any physical interaction between the object applying force and the object experiencing force. Gravity works even when the objects are not in contact. Gravity is an example of the field force.

Universal Law of Gravitation (Gravitational Force)

The universal law of gravitation states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Let’s consider two objects \(A\) and \(B\) of masses \(M\) and \(m\) lie at a distance \(d.\) Then according to the universal law of gravitation, we get:

Formula of Gravitational Force

\(F\propto M \times m\;\)
\(F\propto \frac{1}{{{d^2}}}\)
\(\Rightarrow F = G\frac{{M \times m}}{{{d^2}}}\)
Where \(G\) is the proportionality constant and is known as the universal gravitational constant.
\(G = \frac{{F{d^2}}}{{M \times m}}\)
The SI unit of \(G\) is \({\rm{N}}\;{{\rm{m}}^2}\;{\rm{k}}{{\rm{g}}^{ – 2}}.\) The accepted value of \(G\) is \(6.673 \times {10^{ – 11}}\;{\rm{N}}\;{{\rm{m}}^2}\;{\rm{k}}{{\rm{g}}^{ – 2}}.\)

Gravity vs Gravitational Force

Gravitational force acts between all the objects present on the Earth surface, small or large. It is a weak force. This force can be negligible when the distance between the two objects is infinite, whereas, in the case of gravity, one of two objects must be a celestial body, for example, earth, moon, mars, etc. This force is strong enough to keep an object in the field area. Its value can be zero when an object is at the body’s centre with a larger mass.

Examples of Gravity

1. Gravity binds us to the earth.
2. Gravity allows all objects to stay firmly on the ground.
3. Oceanic tides are formed due to the force of gravity of the moon and the sun on the surface of the water.
4. The gravity of the earth holds the atmosphere on the earth.
5. The force of gravity causes raindrops to fall on the surface of the earth.
6. The force of gravity causes fruits to fall to the ground from trees.

Gravity on the Earth

As the earth is massive, all the objects on the surface of the earth or around its surface are attracted towards its centre. There exists an acceleration due to gravity with which objects fall towards the ground.

Free-fall under Gravity

Whenever an object falls towards the earth under the action of gravity alone, then the object is said to be fallingly. While an object fallsly under gravity there is no change in the direction of motion of the object. But there will be a change in the velocity of the object due to the force of gravity. An acceleration is involved in this case of fall which is known as the acceleration due to gravity. It is denoted by \(g\) and its SI unit is meter per square second \(\left( {{\rm{m\;}}{{\rm{s}}^{ – 2}}} \right).\) Acceleration due to gravity is given by,
\(g = G\frac{M}{{{R^2}}}\)
Where \(M\) is the mass of the earth and \(R\) is the radial distance of the earth.
So, its value is approximately equal to \(9.8\;{\rm{m\;}}{{\rm{s}}^{ – 2}}.\)

Fun fact: If an apple is moving towards the earth, then we might think that the earth should also get pulled towards the apple because of the mutual force of gravitation. But according to Newton’s Second Law of motion, acceleration is inversely proportional to the mass of the object keeping the force constant. Since the mass of the earth is too large as compared to that of the apple, we cannot see the earth moving towards the apple.

Variation of Acceleration due to Gravity

Acceleration due to gravity is not the same at all places. Its value is greater at the poles than the equator because it is inversely proportional to the square of the radius of the earth. The poles are closer to the centre of the earth which makes the value of \(g\) greater at the poles than at the equator.

Motion of Objects Under the Influence of the Earth’s Gravity

All objects, irrespective of their mass, whether they are hollow, big or small, fall on the earth at the same rate. Considering the value of \(g\) as constant, the following are the equations of motion for the uniformly accelerated body:
\(v = u + gt\)
\({v^2} – {u^2} = 2gs\)
\(s = ut + \frac{1}{2}g{t^2}\)

Where \(u\) is the initial velocity of the body, \(v\) is the final velocity of the body, \(t\) is the time for which the body is in the air during its fall and \(s\) is the distance covered by the body. The value of \(g\) will be negative if the body is moving away from the earth’s surface.

How is Weight related to Gravity?

Weight is defined as the force with which an object is attracted towards the centre of the earth because of its gravity. Weight is the product of mass and acceleration due to gravity.

Let \(W\) be the weight of the object, \(m\) be the mass of the object and \(g\) is the acceleration due to gravity, then the weight of the object is given by
\(W = mg\)
It is a vector quantity that always acts towards the centre of the earth. It can be measured in newtons \(\left( {\rm{N}} \right).\)

Gravity Weightlessness

Weightlessness is the condition experienced by a person or object when the effective weight of the body becomes zero. This is usually called a zero-gravity condition. For example, astronauts experience weightlessness because there is no gravity in space.
Objects in space are not massless because mass does not vary from place to place.

Solved Examples on Law of Gravitation

Q.1. The mass of the earth is \(6 \times {10^{24}}\;{\rm{kg}}\) and that of the moon is \(7.4 \times {10^{22}}\;{\rm{kg}}.\) If the distance between their centres is \(3.84 \times {10^5}\;{\rm{km}},\) calculate the force exerted by the earth on the moon. (Take \(G = 6.7 \times {10^{ – 11}}\;{\rm{N\;}}{{\rm{m}}^2}\;{\rm{k}}{{\rm{g}}^{ – 2}}\))
Sol:
The mass of the earth, \(M = 6 \times {10^{24}}\;{\rm{kg}}\)
The mass of the moon, \(m = 7.4 \times {10^{22}}\;{\rm{kg}}\)
The distance between the earth and the moon, \(d = 3.84 \times {10^5}\,{\rm{km}} = 3.84 \times {10^8}\,{\rm{m}}\)
The gravitational force exerted by the earth on the moon will be given by \(F = G\frac{{M \times m}}{{{d^2}}}\)
\(F = \frac{{\left( {6.7 \times {{10}^{ – 11}}} \right) \times \left( {6 \times {{10}^{24}}} \right) \times \left( {7.4 \times {{10}^{22}}} \right)}}{{{{\left( {3.84 \times {{10}^8}} \right)}^2}}}\)
\(\Rightarrow F = 2.02 \times {10^{20}}\;{\rm{N}}\)

Q.2. A sphere of mass \(40\;{\rm{kg}}\) is attracted by another spherical mass of \(15\;{\rm{kg}}\) by a force of \(9.8 \times {10^{ – 7}}\;{\rm{N}}\) when the distance between their centres is \(0.2\;{\rm{m}}.\) Find the value of \(G.\)
Sol:
The mass of the first sphere, \(M = 40\;{\rm{kg}}\)
The mass of the second sphere, \(m = 15\;{\rm{kg}}\)
The distance between the centres of the two spheres, \(d = 0.2\;{\rm{m}}\)
The force of gravitation between the two spheres, \(F = 9.8 \times {10^{ – 7}}\;{\rm{N}}\)
The value of \(G\) is given by the following formula:
\(G = \frac{{F{d^2}}}{{M \times m}}\)
\(G = \frac{{\left( {9.8 \times {{10}^{ – 7}}} \right) \times {{\left( {0.2} \right)}^2}}}{{\left( {40 \times 15} \right)}}\)
\(\Rightarrow G = 6.533 \times {10^{ – 11}}\;{\rm{N\;}}{{\rm{m}}^{\rm{2}}}{\rm{\;k}}{{\rm{g}}^{ – 2}}\)

Based on Newton’s law of gravitation, we can conclude that the force of gravitation is a mutual force that acts between all the objects in the universe. This force of attraction depends on the mass of the interacting objects and the distance between their centres. The gravity of the earth holds all the objects close to its surface including the atmosphere.

Practice Questions on Acceleration Due To Gravity

Study Materials on Embibe

Embibe offers online study materials for Class 8 to Class 12. Students can make use of the following resources to prepare for their exams:

FAQs

We have provided some frequently asked questions about gravity here:

Q.1. Differentiate between acceleration due to gravity and universal gravitational constant.
Ans: Acceleration due to gravity is acquired by a body because of the gravitational pull of the earth. It is a vector quantity and its value changes from place to place. Whereas gravitational constant is equal to the pull force between two point masses of 1 kilogram each separated by a distance of 1 meter. It is a scalar quantity, and its value does not change with the place.

Q.2. Is gravity a theory or a law?
Ans: A scientific theory explains why and how a thing occurs. Since gravity is a natural phenomenon that can be explained, it is a theory. At the same time, the force of gravity follows certain rules and can be stated as a fact because it has a fixed relation with the masses between which it is acting and the distance of their separation, so gravity is also a law.

Q.3. What is the formula of gravity?
Ans: The formula of Gravity is
\(F = G\frac{{M \times m}}{{{d^2}}}\)
Where \(G\) is the proportionality constant and is known as the universal gravitational constant.

Q.4. Is gravity a push or a pull force?
Ans: The force of gravity is a pull force because it always attracts an object towards the centre of the earth or any other object having mass.

Q.5. Define gravitational force.
Ans: Gravitational force is the force that always acts between particles having mass. Gravitational force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centres.