Have you ever found that a ball that you toss up in the air always comes down, however high you toss it? This is a daily experience controlled by one of the most fundamental forces of nature- gravity. As with the mythical fall of an apple that caused Sir Isaac Newton to develop the law of universal gravity, the same principle operates to make things fall on the Earth and planets orbit around the Sun.
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NCERT Class 11 Physics Chapter 7 Notes Gravitation by Careers360 simplifies this interesting concept, dividing the complex concepts into simple explanations. These NCERT notes not only describe the use of gravity in everyday life but also go ahead to further this to planetary motion, satellites and astrophysics. These NCERT Class 11 Physics Chapter 7 Notes Gravitation covered key topics such as: the Law of Gravitation and its uses as presented by Newton, g (acceleration) due to gravity and variations of this, potential energy and gravitational potential, laws of Planetary Motion with examples explained by Kepler, satellite motion and escape velocity of practical importance. These notes are a very crucial study material in CBSE Class 11 Physics board exams, competitive exams such as JEE and NEET, with well-structured theory, solved examples, and practice questions. They are used as a powerful base to learn not just classroom concepts but high-level matters in the space sciences.
Also, students can refer,
This chapter explains the universal law of gravitation, planetary motion using Kepler’s laws, and concepts like gravitational acceleration, potential, and orbital velocity. These Gravitation Class 12 Notes provide clear explanations and formulas, making it easier for students to prepare for CBSE exams as well as competitive exams like JEE and NEET.
Mathematical Form
If m1 and m2 are the particles’ masses and the distance between them is r, the force of attraction F among the particles is given by
F∝m1m2r2∴F=Gm1m2r2
(G is the universal constant of gravitation.)
Vector Form
The force F21 exerted on the particle m2 by the particle m1 is given by:
F→21=−Gm1m2r2r12^
Where r^12 is a unit vector drawn from particle m1 to particle m2
Similarly,
F→12=−Gm1m2r2r21^
G=Fr2m1m2
newton ( metre )2( kg)2
dyne( cm)2gm2
G=6.67×10−11Nm/kg2
[G]=[M1L1T2][M0L0T0][M2L0T0]=[M−1L3T−2]
g=GMR2
g′∝1r2
Where r=R+h
g′=g(RR+h)2=g(1+hR)−2g′=g[1−2hR]
g=GMR2=43πρgR
And g′∝(R−d)
This means the value of g' decreases on going below the surface of the earth.
So g′=g[1−dR]
The gravitational potential at any place in a gravitational field is defined as the work necessary to transfer a unit mass from infinity to that point.
⇒V=−GMr
P.E.=−GMmr
1. Because the moon revolves around the Earth, it is considered a satellite. Jupiter has a total of sixteen satellites orbiting it. These satellites are referred to as natural satellites.
2. A human-built artificial satellite is one that has been sent into a circular orbit. The first satellite, SPUTNIK-I, was launched by the Soviet Union, whereas the first satellite, ARYABHATTA, was launched by India.
Assume that a satellite is launched from the Earth's surface using a single-stage launch method. Once the rocket's fuel is ignited, the rocket begins to ascend. The rocket reaches its maximum velocity when all of the fuel has been used up.
1. The rocket escapes into space with the satellite if its maximum velocity is equal to or greater than the escape velocity, exceeding the Earth's gravitational force.
2. If the rocket's greatest velocity is less than escape velocity, it will be unable to defy the Earth's gravitational attraction, and both the rocket and the satellite will eventually crash to the ground.
As a result, a single-stage rocket will not be able to place a satellite into a circular orbit around the Earth. As a result, a launching device is required to place a satellite into a circular orbit around the Earth.
Expressions for Different Energies of Satellite
1. Potential Energy (P.E.):
The satellite is at a distance (R + h) from the centre of the Earth.
U=−Gm1m2r⇒−GMmR+h=U
2. Kinetic Energy (K.E.):
The Revolution of satellites around a circular orbit has having critical velocity (vc). Hence, its kinetic energy is given by:
K.E.=12mvc2vc=GMR+h⇒K⋅E⋅=12m(GMR+h)=GMm2(R+h)
3. Total Energy (T.E.):
T.E.=−GMmR+h+GMm2(R+h)=−GMm2(R+h)
4. Binding Energy (B.E.)
T.E. = -(B.E.)
Kepler gave three laws of planetary motion. They are:
r3/T2= constant
When a satellite is lifted to a specific height above the Earth and then projected horizontally, the following four scenarios may occur, depending on the amount of horizontal velocity.
1. If the projection velocity is smaller than the critical velocity, the satellite will move in an elliptical orbit, but the point of projection will be apogee, and the spacecraft will approach the earth with its perigee point at 180o. If it enters the atmosphere as it approaches perigee, it loses energy and spirals downward. It will continue to fly in an elliptical orbit if it does not enter the atmosphere.
2. If the projected velocity achieves the critical velocity, the satellite will move in a circular orbit around the planet.
3. The satellite will be in an elliptical orbit with an apogee greater than the predicted height if the projected velocity is more than the critical velocity but less than the escape velocity.
4. The satellite goes in a parabolic path if the projection velocity is equal to the escape velocity.
5. If the projection velocity is greater than the escape velocity, the orbit will become hyperbolic, escaping the Earth's gravitational attraction and continuing to travel indefinitely.
Assume that a mass m satellite is elevated to a height h above the earth's surface and then projected horizontally with an orbital velocity vo. The satellite starts moving around the globe in a circular orbit with a radius of R + h, where R is the Earth's radius.
The gravitational force acting on the satellite is GMm(R+h)2
where M is the mass of the earth and Gis the constant of gravitation.
For circular motion,
Centrifugal force = Centripetal force
mvo2(R+h)=GMm(R+h)2∴vo=GM(R+h)
Kinetic Energy of projection = Binding Energy
12mve2=GMmr⇒ve=2GMR=2gR
1. A feeling of weightlessness is similar to a moving satellite since it alludes to the gravitational force that draws a body towards the Earth's centre. It isn't due to the fact that the weight is zero.
2. A gravitational pull is exerted on an astronaut when he is on the surface of the Earth. This gravitational force is equal to an astronaut's weight, and an astronaut exerts this force on the Earth's surface. The earth's surface produces an equal and opposite reaction, and he feels his weight on the ground as a result of this reaction.
3. An astronaut on an orbiting spacecraft experiences the same acceleration towards the Earth's centre as the satellite, and this acceleration is equal to the acceleration due to the Earth's gravity.
As a result, the astronaut has no impact on the satellite's floor. The astronaut, of course, is unaffected by the floor's reaction force. Because there is no reaction, the astronaut has a sense of weightlessness. (In other words, he has no concept of how heavy he is.)
Q1: If the mass of the sun were ten times smaller and the gravitational constant G were ten times larger in magnitude
a) walking on ground would become more difficult
b) the acceleration due to gravity on earth will not change
c) raindrops will fall much faster
d) aeroplanes will have to travel much faster
Answer:
If G′=10G
And Ms′=Ms10
Then g′=G′MEr2=10GMr2=10g
Weight of a person =mg′=10mg
Hence statement (a) is correct, and statement (b) is incorrect
Fon man due to sun =GMs′mr2=GMsm10r2
The terminal velocity vTαg′ or vTα10g
Hence raindrops fall 10 times faster. Option statement (c) is correct
In order to maintain the speed after the increase in gravitational force, the aeroplane will have to travel faster.
Hence, the answer is the options (a), (c) and (d)
Q2: If the law of gravitation, instead of being an inverse-square law, becomes an inverse-cube law
a) planets will not have elliptic orbits
b) circular orbits of planets are not possible
c) projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic
d) there will be no gravitational force inside a spherical shell of uniform density
Answer:
If the law of gravitation suddenly changes and becomes an inverse cube law, then the law of areas still holds. This is because the force will still be a central force, due to which the angular momentum will remain constant.
Also, for a planet of mass m revolving around the sun of mass M, we can write according to the question,
F=GMma3=mv2a
[∵ Centripetal force, mω2a=mv2a]
where a is the radius of the orbiting planet.
Orbital speed, v=GMa⇒v∝1a
Time period of revolution of a planet,
T=2πrv
On putting in the value of orbital speed, we get
T=2πaGMa=2πa2GM⇒T2∝a4
Hence, the orbit of the planet around the sun will not be elliptical because for an elliptical orbit T2∝a3.
Hence, the orbit of the planet around the sun will not be circular because for a circular orbit T2∝a3.
As force F=(GMa3)m=g′m, where g′=GMa3.
Since, g′= acceleration due to gravity is constant, hence path followed by a projectile will be approximately parabolic ( as T∝a2 ).
Hence, the answer is the options (a), (b) and (c).
Q3: Which of the following options is correct?
a) acceleration due to gravity decreases with increasing altitude
b) acceleration due to gravity increases with increasing depth
c) acceleration due to gravity increases with increasing latitude
d) acceleration due to gravity is independent of the mass of the earth
Answer:
g at an altitude g(1−2hR)
Acceleration due to gravity decreases with increasing altitude. Hence, statement (a) is correct
gλ=g−ω2R(cosλ)2
As cos is a decreasing function, the value of gravity increases with an increase in latitude, i.e. from the equator to the pole. Hence, statement (c) is correct
g=GMR2 where M is the mass of the Earth. Hence, statement (d) is incorrect
Hence, the answer is options (a) and (c).
Strong Foundation of Gravitation Concepts
Simplified Explanation of Complex Topics
Time-Saving Revision Resource
Increases Competitive Exam Preparation (JEE and NEET)
Helps in scoring higher marks in CBSE Exams
Fast access to useful Formulas and Derivations
Bridges Class 11-12 Physics Learning
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NCERT Class 11 Notes Chapter-Wise are designed to help students revise important topics, formulas, and concepts in a structured way. These notes cover all chapters from Physics, Chemistry, Maths, and Biology as per the latest CBSE syllabus, making them useful for both board exams and competitive exams like JEE and NEET.
Frequently Asked Questions (FAQs)
While NCERT gives a detailed theory, these notes provide a simplified summary, quick revision points, and exam-oriented explanations, which save time during preparation.
A gravitational field is the region around a mass where it exerts a force on other masses. It is calculated as the gravitational force per unit mass at a point.
Kepler’s laws explain the motion of planets around the Sun and form the foundation of orbital mechanics used in astronomy and satellite systems.
Yes, the notes are prepared in alignment with the CBSE and NCERT syllabus and also focus on conceptual clarity, which is crucial for exams like JEE, NEET, and other competitive tests.
The NCERT notes for Class 11 Physics chapter 7 do not include any derivations. This NCERT note summarizes the chapter's important points and equations and can be used to review the gravitation.
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