Content Curator
Gravity also termed as Gravitation, is a property due to which any two bodies in the universe having mass attract each other. The force with which the two bodies attract each other is known as Gravitational force or Force of Gravitation. Sir Issac Newton proposed that all particles or objects in the universe attract each other in the same manner as the earth attracts apples.
- Gravity is a fundamental force in nature that causes the mutual attraction between the two bodies having masses.
- Among four fundamental forces, gravity is the weakest force i.e. approx 1038 times weaker than the strong nuclear force.
- Although it has no significant role at the subatomic level, it has great importance at the macroscopic level to determine the motion of the planets, stars, and galaxies.
| Table of Content |
Key Terms: Gravitational force, Gravitational constant, Gravity, Acceleration due to Gravity, Weight, Value of G, Centrifugal force, Distance, Law of Gravitation
What Is Gravity?
[Click Here for Sample Questions]
Gravity is a property due to which any bodies having mass attract each other. The force generated due to gravity is termed to be the gravitational force.
- The gravity of the sun kept the Earth in the orbit of the sun.
- The atmosphere and the air in which we live are held by gravity.
- The gravitational force between the earth and the moon helps the moon to revolve around the Earth.
- Also, Weight of the any physical object on the earth is due to gravity.
- The gravity of the moon causes sublunar tides in the ocean.
- On Earth, the force of gravity is the result of two forces i.e. the gravitational force and the centrifugal force.
- The range of gravity is infinite, although its influence becomes weaker at a farther distance.
Gravity
Video Explanation of Gravity
Gravitation Detailed Video Explanation
Gravity Formula
[Click Here for Sample Questions]
The gravity formula is applicable for non-zero masses. The gravity formula is given by
\(F=G \frac {m_1m_2}{r^2}\)
Where
- F = Gravitational force
- m1 = mass of the first body
- m2 = mass of the second body
- r = distance between the two masses
- G = Universal Gravitational Constant (Value of G is 6.67 x 10-11 Nm2kg-2)
Gravitational Force Between Two Objects
Derivation of Gravity Formula
[Click Here for Sample Questions]
According to the universal law of gravitation, every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particle and the square of the distance between the particles.
Consider two bodies of masses m1 and m2 are separated by distance r, then according to the law of gravitation force between the two bodies is
F α m1m2
And, F α1/r2
By combining the above two equations, we get
F α \(\frac{m_1m_2}{r^2}\)
\(\Rightarrow F=G\frac{m_1m_2}{r^2}\)
Where G is a constant known as Universal Gravitational Constant.
Example of Gravitational Force
This law holds good irrespective of the nature of the two bodies at all places and at all times throughout the universe. That is why it is known as the Universal Law of Gravitation.
The gravitational force between two bodies is equal in magnitude but opposite in direction i.e. they form action-reaction pairs. Hence, the gravitational force is Newtonian in nature.
Gravity Formula
Characteristics of Gravitational Force
[Click Here for Sample Questions]
Following are the characteristics of Gravitational force
- Gravitational force is a central force i.e. it acts along the line joining the centers of the two interacting bodies.
- The gravitational force between two bodies forms an action and reaction pair i.e. the force is equal in magnitude but opposite in direction.
- The gravitational force between two bodies is independent of the nature of the intervening medium.
- Gravitational force is a long-range force
- It is a conservative force.
Also Read-
| Force of Attraction Formula | Gravitational Acceleration Formula | Gravitational Force and Law of Gravitation |
| Gravitation Laws | Value Of G | Gravitation Vs Gravity |
Acceleration due to Gravity
[Click Here for Sample Questions]
The acceleration produced in the motion of the body under the effect of gravity is called acceleration due to gravity. It is denoted by “g”.
The formula for the acceleration due to gravity on the surface of the earth is given by
\(g=\frac {GM_e}{R_e^2}\)
Where
- G = Gravitational constant
- Me = Mass of the earth
- Re = Radius of the earth
The value of acceleration due to gravity on the surface of the earth is 9.8 m/s2.
The formula for the acceleration due to gravity above the surface of the earth is given by
\(g_h=g[1-\frac {2h}{R_e}]\)
Where
- gh = Acceleration due to gravity at height h
- g = Acceleration due to gravity on the surface of the earth
- Re = Radius of the earth
The formula for the acceleration due to gravity below the surface of the earth is given by
\(g_d=g[1-\frac {d}{R_e}]\)
Where
- gd = Acceleration due to gravity at depth d
- g = Acceleration due to gravity on the surface of the earth
- Re = Radius of the earth
Also Read:
Solved Examples
[Click Here for Sample Questions]
Ques. What is the gravitational force between the bodies of masses, m1= 10 Kg and m2 = 40 kg separated at a distance of 5 m?
Ans. The formula for gravitational force between two bodies is given by
\(F=G\frac{m_1m_2}{r^2}\)
Given
- m1 = 10 kg
- m2 = 40 kg
- r = 5 m
On substituting the values, we get
F = 6.674 × 10−11 x 10 x 40/(52)
⇒ F = 1.06 x 10-9 N
Ques. If the masses of the two bodies are quadrupled and the distance between their centers is doubled, then how many times the force of gravitation between them will be changed?
Ans. Let the masses of the two bodies are m1 and m2 and initially, the distance between them is r, then the force of gravitation between the two masses is given by
\(F_1=G\frac{m_1m_2}{r^2}\)
Now, when both masses become 4 times i.e. quadrupled and the distance between them is doubled, then the force of gravitation between the two masses is given by
\(F_2=G\frac{4m_1 \times 4m_2}{(2r)^2}\)
\(\Rightarrow F_2=4 \times G\frac{m_1m_2}{r^2}\)
\(\Rightarrow F_2=4 \times F_1\)
Hence, the gravitational force is increased by 4 times the initial value.
Things to Remember
- Gravity is a property of masses of two bodies due to which they can attract each other by a force known as gravitational force.
- Gravitational force can be explained as the force between two non-zero mass units or objects.
- The gravitational constant is represented by ‘G’, where G = 6.674×10−11 m3 kg-1 s-2
- The gravitational Formula is
\(F=G\frac{m_1m_2}{r^2}\)
- The larger the mass of the body, the larger the value of the gravitational force between the bodies.
- Gravitational force is Newtonian in nature.
Sample Questions
Ques. What is the gravitational force between the bodies of masses, M1= 20 Kg and M2 =30 kg? The distance by which the bodies are separated is 10m. (2 Marks)
Ans. We have, F = \(G\frac{m_1m_2}{r^2}\)
F = 6.674 × 10−11 x 20 x 30/(102)
F = 6.674 × 10−11 x 6
⇒ F = 40.044 x 10(-11) N
Ques. Can gravity create the waves? (1 Mark)
Ans. Yes, gravity can create waves.
Ques. Which is the strongest force? (1 Mark)
Ans. The nuclear force is the strongest force.
Ques. The gravitational force between the bodies of masses, M1= 20 Kg and M2 = 30 kg is F = 30 Kg m s-2. Find the distance by which the bodies are separated. (2 Marks)
Ans: We have, F = \(G\frac{m_1m_2}{r^2}\)
⇒ 30 = 6.674×10−11 x 20 x 30/(r2)
r2=20 x 6.674×10−11
r2 = 13.348 x 10-10
⇒ r = 3.65 x 10-10 m.
Ques. Why does the moon's gravity cause tides on Earth? (2 Marks)
Ans. The moon is closer to the earth and thus the gravitational force between the earth and the moon is short. The ocean water responds to the shorter force effectively and thus it results in tides in the oceans on the earth.
Ques. The gravitational force between the bodies of masses, M1= m Kg, and M2 = 30 kg is F = 30 Kg m s-2. The distance by which the bodies are separated is r = 20 m. Find m? (2 Marks)
Ans. We have F = \(G\frac{m_1m_2}{r^2}\)
⇒ 30 = 6.674×10−11 x 30 x m/(202)
⇒ m = 400/6.674×10−11
⇒ m = 2669.6 x 10−11 Kg
Ques. Why is gravity absent in space? (2 Marks)
Ans. Gravity is present in space. However, the gravitational force in space is smaller than the Earth. As one moves farther from the Earth and thus the gravity in space becomes weaker than the Earth and it feels negligible in space.
Ques. The gravitational force between the bodies of masses, M1= 50 Kg and M2 = 40 kg is F = 30 Kg m s-2. Find the distance by which the bodies are separated. (2 Marks)
Ans. We have F = G M1M2/(r)2
⇒ 30= 6.674×10−11 x 50 x 40/(r2)
⇒ r2 = 200 x 6.674 ×102/3
⇒ r2= 400 x 10-11
⇒ r=2 x 10-3 m.
Ques. The gravitational force between the bodies of masses, M1 = 40 Kg and M2 = 40 kg is F = 30 Kg m s-2. Find the distance by which the bodies are separated. (2 Marks)
Ans. We have F = G M1M2/(r)2
⇒ 30 = 6.674 × 10−11 x 40 x 40/(r2)
⇒ r2 = 160 x 6.674 × 10−11/3
⇒ r2 = 320 x 10-11
⇒ r = 5.65 x 10-5 m.
Question: The gravitational force between the bodies of masses, M1= x Kg, and M2=20 kg is F= 30 Kg m s-2. The distance by which the bodies are separated is r=20m. Find m? (2 Marks)
Ans. We have F = G M1M2/(r)2
⇒ 30 = 6.674×10−11 x 20 x m/(202)
⇒ m = 600/6.674×10−11
⇒ x = 0.899 x 10−11 Kg.
Also Read:
Comments