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Gravitational Force is a universal force of attraction acting between any two objects having mass.
- It is one of the four fundamental forces in the universe along with the weak force, the strong force, and the electromagnetic force.
- It is a force that attracts any two bodies in the universe whether they have equal masses or not.
- The SI unit of gravitational force is Newton (N).
- The concept of gravitational force was proposed by Sir Issac Newton.
- Gravitational Force is also known as Gravity.
Gravitational Force Formula is given as
| \(F_g = \frac{Gm_1m_2}{r^2}\) |
Here, Fg refers to the gravitational force, m1 and m2 are the masses of the two objects, r2 is the distance between the center points of the objects and G is the gravitational constant.
Read More: NCERT Solutions for Class 11 Physics Gravitation
Key Terms: Gravitational Force, Gravitational Force Formula, Gravitation, Universal Law of Gravitation, Gravity, Force, Center of Mass
What is Gravitational Force?
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Gravitational Force is the force of attraction exerted by different objects on one another due to their masses.
- It is defined as the force that pulls everything toward the earth's surface.
- It is a fundamental force that attracts all matter around us such as the planets, stars, galaxies, and light.
- It was proposed by Sir Isaac Newton in his universal law of gravitation.
- Gravitational force is responsible for the motion of the planets and the Moon.
- Due to the large separation distance, it is a weak force that cannot be detected.
- It determines the weight of all physical objects on earth.
Gravitational Force
According to Newton’s Universal Law of Gravitation, the Gravitational Force is defined as
| "The force of attraction between any two particles in the universe is exactly proportional to the product of their masses and inversely proportional to the square of their distance." |
Thus, Gravitational Force is
- Inversely proportional to the square of the distance between the center of mass of the given objects.
- Directly proportional to the product of the masses of the given objects.
Gravity Video Lecture
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Gravitational Force Formula
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Gravitational Force Formula is also referred to as Newton’s Law of Gravitation. It gives the magnitude of the force between two objects.
The Gravitational Force Formula is expressed as:
| \(F_g = \frac{Gm_1m_2}{r^2}\) |
Where
- Fg: Gravitational Force acting between m1 and m2.
- G: Gravitational Constant whose value is 6.67 × 10 -11m3/kg.s2.
- m1 and m2: Masses of given two objects.
- r: Distance between the centers of two objects.
Read More: Value of G
Solved Examples on Gravitational Force Formula
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Given below are a few solved examples on Gravitational Force Formula to understand the formula in a better manner:
Example 1: What will be the gravitational force of attraction between a man of mass of 50 kg and a bus of mass of 1500 kg, if the distance between them is given as 10 m?
Solution: Given that
- Mass of First Man, m1 = 50 kg
- Mass of Second Man, m2 = 1500 kg
- Distance between Them, r = 10 m
- Gravitational Constant, G = 6.67259 x 10–11 N m2/kg2
Using the Gravitational Force Formula,
\(F_g = \frac{Gm_1m_2}{r^2}\)
Substituting the given values in the Gravitational Force Formula, we get
Fg = [6.673 ×10–11 × 50 × 1500] / 102
Fg = 5.0025 x 10-8 N
Thus, the gravitational force between both men is 5.0025 x 10-8 N.
Read More: Gravitation Important Questions
Example 2: The mass of the Earth is given as 6 × 1024 kg and the distance between the Earth and the Sun is 1.5 × 1011 m. What will be the mass of the sun if the gravitational force between the two is 3.5 × 1022 N?
Solution: According to the question,
- Mass of Earth, me = 6 × 1024 kg
- Distance between Earth and Sun, r = 1.5 × 1011 m
- Gravitational Force Between Earth and Sun, F = 3.5 × 1022 N
- Gravitational Constant, G = 6.67259 x 10–11 N m2/kg2
- Mass of Sun, ms =?
Substituting the given values in the Gravitational Force Formula,
\(F_g = \frac{Gm_1m_2}{r^2}\)
3.5 ×1022 = [6.673 ×10–11 × 6 × 1024 × ms] / (1.5 × 1011)2
ms = 1.967 × 1030 kg
Thus, the mass of the sun is 1.967 × 1030 kg.
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Things to Remember
- Gravitational Force is the fundamental force of attraction between two masses in the universe.
- It shows how everything in the universe is attracted to something else with some force.
- Gravitational Force is proportional to the masses of the objects.
- It is inversely proportional to the square of the distance between the centers of mass.
- Gravitational Force Formula is given as \(F_g = \frac{Gm_1m_2}{r^2}\).
- It is responsible for the attraction of objects toward the center of the Earth.
Read More: Gravitation MCQs
Previous Years’ Questions
- Gravitational field is… (Haryana PMT 2009)
- Three uniform spheres of mass M and radius R earth are kept in such…
- Gravitational force is required for… (NEET 2000)
- The dimensional formula for the gravitational constant… (BCECE 2005)
- What will be the formula of mass of the earth in terms… (NEET 1996)
- The acceleration due to gravity at a height of 1km above the earth… (NEET 2017)
- The work done in shifting a particle of mass… (UP CPMT 2011)
- If suddenly the gravitational force of attraction between earth… (JMI-EEE 2005)
- The force of gravitation is… (AIIMS 2007)
- A man of 50 kg mass is standing in a gravity-free space at a… (NEET 2010)
- Assuming that the gravitational potential energy of an object… (NEET 2019)
- A body starts to fall freely under gravity. The distance… (Chhattisgarh PMT 2004)
- If the gravitational force between two objects were proportional… (NEET 1994)
- Two astronauts are floating in gravitational-free space after… (NEET 2017)
Sample Questions
Ques. Calculate the gravitational force acting on a body at the earth’s surface if the mass of the body is 1000 Kg, the mass of the earth is 5.98 x 1024 kg and the radius of the earth is 6.38 x 106 m. (3 Marks)
Ans. Given that
- Mass of the Body, m1 = 1000 kg
- Mass of the Earth, m2 = 5.98 x 1024 kg
- Distance between Earth and Body, r = 6.38 x 106 m
- Gravitational Constant, G = 6.67 x 10–11 N m2/kg2
Using the Gravitational Force Formula,
\(F_g = \frac{Gm_1m_2}{r^2}\)
Fg = [6.67 ×10–11 × 1000 × 5.98 x 1024] / ( 6.38 x 106)2
Fg = [39.8 ×1016] / [40.7 × 1012]
Fg = 0.9778 x 104
Fg = 9.778 N
Thus, the force of gravity acting on the body at the surface of the earth is 9.778 N.
Ques. What will be the gravitational force if two objects with masses 30 kg and 50 kg are separated by a distance of 4m? (3 Marks)
Ans. It is given that
- Mass of First Object m1 = 30 kg
- Mass of Second Object m2 = 50 kg
- Distance between Both Objects r = 4m
- G = 6.67259 x 10–11 N m2/kg2
Using the Universal Gravitation Formula,
\(F_g = \frac{Gm_1m_2}{r^2}\)
Fg = [6.673 ×10–11 × 30 × 50] / 16
F = 62.55 x 10–11N
Thus, the gravitational force between the two objects is 62.55 x 10–11N.
Ques. What is Gravity? (3 Marks)
Ans. Isaac Newton defined gravity as the force that pulls all objects around the Earth's surface towards its center. It is best explained by Albert Einstein's general theory of relativity, which characterizes gravity as a curvature of space-time induced by the uneven distribution of mass rather than a force. Gravitational force is the relation between the masses of two objects and the square of the distance between them.
Ques. What is the difference between Gravitational Constant and Acceleration due to Gravity? (3 Marks)
Ans. The universal gravitational constant is defined as the force of attraction between two objects of equal mass separated by an equal distance anywhere in the universe. The value of the gravitational constant is 6.67259 x 10–11 N m2/kg2. Gravitational acceleration is defined as the acceleration experienced by a body in free fall because of the vast body's gravitational force. The value of the acceleration of gravity is 9.8 m/s2.
Ques. What is the formula for Gravitational Force? (3 Marks)
Ans. The gravitational force formula is as follows:
\(F_g = \frac{Gm_1m_2}{r^2}\)
Here
- F is the gravitational force acting between two objects.
- m1 is the mass of the first object.
- m2 is the mass of the second object.
- r is the distance between the centers of two objects.
Ques. What is the source of centripetal force required for a planet to revolve around the Sun? What factors influence that force? (2 Marks)
Ans. The source of centripetal force necessary to rotate around the sun is gravity. The distance between the planet and the sun, as well as their masses, determines this force. The planet would shift to move tangentially outwards to the circular route if this force became zero due to the absence of centripetal force.
Ques. Calculate the gravitational force if the mass of two bodies is 80 kg and 200 kg respectively. Both bodies are separated from each other by a distance of 6m. (3 Marks)
Ans. According to the question,
- Mass of First Body m1 = 80 kg
- Mass of Second Body m2 = 100 kg
- Distance between the Bodies r = 6 m
- G = 6.67259 x 10–11 N m2/kg2
Using the Gravitational Force Formula,
\(F_g = \frac{Gm_1m_2}{r^2}\)
F = [6.673×10–11× 80 × 100] / 36
F = 148.28×10–11 N
Thus, the gravitational force between both bodies is 148.28 × 10–11 N.
Ques. If the distance between the Earth and the Sun was half its present value, the approximate number of days in a year on the Earth would have been:
(a) 182.5 days
(b) 129 days
(c) 64.5 days
(d) 730 days (3 Marks)
Ans. (b) 129 days
- Let the present time period of revolution of the earth be T1, i.e. 365 days
- Let T2 be the time period of revolution when the distance between the Sun and the Earth is halved.
- Let R1 be the present radius of revolution and R2 be the radius of revolution when the distance is halved.
Therefore, R1 = 2R2
According to Kepler's law of the period, R3 ∝ T2 → T ∝ R3/2
⇒ T1/T2 = (R1/R2)3/2 = (R1/R1/2)3/2 = 2√2
⇒ T2 = T1/2√2 = 365/2√2 days = 129 days
Hence, the time period of revolution of the earth will be 129 days if the distance between the Earth and the Sun is halved.
Ques. The earth is drawn to an apple, and the apple is drawn to the earth's center. So, why does the apple merely fall toward the ground, but the earth does not move toward the apple? (2 Marks)
Ans. Both the apple and the earth are subjected to the same gravitational forces. The acceleration created by the apple is the same as that produced by the earth's magnitude. Because the apple's mass is so small in comparison to the earth's, this is insignificant. As a result, the earth's motion goes unnoticed.
Ques. State a few properties of Gravitational Force. (3 Marks)
Ans. The properties of gravitational force are listed as follows:
- It pulls together two objects or bodies rather than pushing them away.
- It is proportional to the masses of the objects.
- It is a long-distance force always present between two objects irrespective of their medium.
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