Gravitation - Notes, Topics, Formulas, Books, FAQs

Edited By Team Careers360

Have you ever wondered how you can walk on the ground freely ? or when a fruit falls from a tree or something drops from a height, it always heads for the ground? This is exactly what Sir Isaac Newton wondered and offered the world the concept of gravitation. In simple words, Gravitation is the force operating between two objects on the earth. So any thrown object will be attracted toward the earth and will fall on earth. The gravitational force has a very important role which allows us to live in this wonderful world. If gravity disappeared suddenly then we would all start to float immediately. So it is very important to study about Gravitational. And this chapter will help you to understand various laws, various properties of gravitational force along with the application of these laws and properties.

Gravitation is one of the most important chapters from mechanics while preparing for all competitive exam. Because it helps you to understand about gravitational force, field, etc which is the basis of many theories which we study under physics. Gravitation is easy to understand and a high scoring topic. You will get at least one question from this chapter. Gravitation and Electrostatics are conceptually similar to each other so when you study Electrostatics after studying gravitation, you will understand its concepts easily. The Concept of Gravitation and other chapters of mechanics are mixed in miscellaneous questions which are asked in competitive exams.

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Notes on Gravitation-

So we will discuss step by step about important topics from this chapter followed by an overview of this chapter.

Then we will understand important formulas from this chapter. Remembering these formulas will increase your speed while question-solving.

Gravitation Topics

The universal law of gravitation.
Acceleration due to gravity
Kepler's laws of planetary motion.
Gravitational potential energy; gravitational potential.
Escape velocity. Orbital velocity of a satellite. Geostationary satellites.

Overview of Gravitation

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Newton's Law of Gravitation-

Gravitational force is an attractive force acting between two masses m_1 and m_2 separated by a distance r. This force is directly proportional to the m_1*m_2 and inversely proportional to r^2 .

After studying that Gravitation force operates between any two objects on the earth, You may wonder and ask why not all bodies attract each other and stick together due to gravitational force. So answer to this question is that Gravitational Force is the weakest among all the four fundamental forces known to us till now. Let Suppose 2 similar ball of mass 1 kg are placed 1m apart then the gravitational force acting between them is simply G which is equal to $6.6710*10^{-11} Nm^2 (kg)^{-2}$ As you see this is a very negligible attractive force.

In this chapter, you will learn about various concept regarding acceleration due to gravity (g) with its definitions and suitable example.

Height, Depth, Shape of earth, Rotation of earth are the important factors which affect the value of g.

Let's have a look at how g value changes due to the shape of the earth.

$R_{e}\rightarrow$ Radius of equator

$R_{p}\rightarrow$ Radius of pole

$R_{equator} > R_{pole}$

Equatorial radius is about 21 km longer than the polar radius.

So $g_{pole} > g_{equator}$

In fact

$g_{p}=g_{e}+0.018m/s^{2}$

Or we can say that Weight increases as the body are taken from equator to pole.

You will also learn about satellites and their motion in space. You will also learn to calculate their orbital velocity, their escape velocity, etc.

Related topics,

Formulas for Gravitation

Gravitational force-

$F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}$

Acceleration due to gravity (g)

$g=\frac{GM}{R^{2}}$

Variation in 'g' with height

$g'\alpha\, \frac{1}{r^{2}}$

r=R+h

Variation in 'g' with depth

$g'\alpha (R-d)$

$g'=g\left [ 1-\frac{d}{R} \right ]$

Variation in 'g' due to Rotation of earth

$g'=g-\omega ^{2}R\cos ^{2}\lambda$

Gravitational field Intensity

$\vec{I}=\frac{\vec{F}}{m}$

Where F=Gravitational force

Gravitational Potential

$V=-\int \overrightarrow{I}\cdot \overrightarrow{dr}$ or $V=-\frac{W}{m}=-\int \frac{\overrightarrow{F}\cdot \overrightarrow{dr}}{m}$

Work done against gravity

$W=\Delta U=GMm\left [ \frac{1}{r_{1}}-\frac{1}{r_{2}} \right ]$

Escape velocity

$V_{c}=\sqrt{\frac{2GM}{R}}$

Escape energy

$\frac{GMm}{R}=Escape \; Energy$

Kepler's 2nd law

$\frac{dA}{dt}= \frac{L}{2m}$

Kepler's 3rd law

$T^{2}\: \alpha\: a^{3}$

or $T^{2}\: \alpha \: \left ( \frac{r_{1}+r_{2}}{2} \right )^{3}$

Energy of satellite

$E=-\frac{GMm}{2r}$

How to prepare Gravitation

First, you should have good command over the concepts of Gravitation and you should also know how to apply them well at the time of the entrance exam or while solving questions. Please try to understand each concept from this chapter, with the help of theory, questions with solutions and video lectures on each important concept.
For each concept practice enough problems to have a thorough understanding of the concept. Solve all the questions at home with proper concentration and try to do all calculations by yourself without seeing the solution first. Through practice, you will come to know how to approach a question

Concepts like Newton's Law of Gravitation, Acceleration due to gravity, Gravitational potential energy, Kepler’s laws of planetary motion, Escape velocity, etc are the most important concept from this chapter with respect to various competitive exam.
Acceleration due to gravity plays a very important role to understand other concepts and solve problems easily from this chapter.
Understand all the laws from this chapter along with their applications. With proper study, you can solve questions from this chapter with ease.

NCERT Notes Subject Wise Link:

Gravitation Tips

Make a plan to prepare for this chapter and Stick to a Timetable.
Study the concept first and then start solving questions. Don't go through question directly without knowing the concept.
Solve previous year question of various exam from this chapter.
Use smart methods to solve questions.

NCERT Solutions Subject wise link:

NCERT Exemplar Solutions Subject wise link:

Books for Gravitation

For Gravitation, chapter concepts in NCERT are enough but you will have to practice lots of questions including previous year questions and you can follow other standard books available for competitive exam preparation like Concepts of Physics (H. C. Verma) and Understanding Physics by D. C. Pandey (Arihant Publications).

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