NCERT Class 11 Physics Chapter 8 Notes Gravitation - Download PDF

Revision Notes for CBSE Class 11 Physics Chapter 8 Gravitation - Free PDF Download

Welcome to the reliable Gravitation class 11 notes prepared by Careers360's subject experts! Our Chapter 8 notes on Gravitation for Class 11 Physics are an invaluable resource for both board exams and competitive tests such as JEE and NEET. These meticulously crafted class 11 physics chapter 8 notes delve into the complexities of gravitational force, elucidating its importance in the universe.

From galaxies to meteoroids, every celestial component is examined, providing a thorough understanding of this natural phenomenon. Sir Isaac Newton's Principia Mathematica paved the way for understanding gravity, and our Gravitation notes class 11 cover the basics, such as the inverse-square law and fundamental equations.

Furthermore, these meticulously curated cbse class 11 physics ch 8 notes are available in PDF format, making them accessible without the need for an internet connection. Prepare for your engineering exams with ease, as our notes enable you to excel time and again, free of charge. Additionally, with NEET allocating a 2% weightage to this chapter and JEE typically featuring one question from it, our ch 8 physics class 11 notes provide invaluable insights to help you ace these competitive exams.

Also, students can refer,

• NCERT Solutions for Class 12 Physics Chapter 8: Gravitation
• NCERT Exemplar Solution Class 12 Physics Chapter 8: Gravitation

Newton's Law of Gravitation

Definition

Every particle of matter attracts each other with a force proportional to its masses multiplied by the square of its distance.

Mathematical Form

If m₁ and m₂ are the particle’s masses and the distance between them is r, the force of attraction Famong the particles is given by

(G is the universal constant of gravitation.)

Vector Form

The force F₂₁ exerted on the particle m₂ by the particle m₁ is given by:

Where r₁₂ cap is a unit vector drawn from particle m₁ to particle m₂

Similarly,

• Universal Constant for Gravitation

The universal gravitation constant is given as

S.I. unit

C.G.S. unit

Value of G

Dimensions of G

• Variation in ‘g’

Condition: Gravitational Acceleration Above the Earth's Surface

Let M and R be the mass and radius of the earth, respectively, and g signify the gravity-induced acceleration at the surface. Assume a mass of m is placed on the surface of the earth.

The body's mass,' mg,' is the same as the gravitational force acting on it.

Assume the body is now raised to a height h above the earth's surface, its weight is now mg, and the gravitational force acting on it is:

Dividing,

Gravitational acceleration at a Very Small Height

If h << R, then neglecting the high powers of ‘h’ we get

• Satellite

A satellite is a smaller body that spins around a larger body under the influence of its gravitation. It could be natural or man-made.

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.

Minimum Two-Stage Rocket is Used to Project a Satellite in a Circular Orbit Around a Planet

Assume that a satellite is launched from the earth's surface using a single-stage launching method. Once the rocket's fuel is ignited, the rocket begins to ascend. The rocket reaches its maximum velocity when all of the fuels have 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.

Kepler’s law:

Kepler gave three laws of planetary motion. They are:

• First law: All planets revolve in an elliptical orbit with the Sun as focus.

• Second law: Irrespective of the orbit, the planet covers equal areas in equal intervals of time.

• Third law: The orbital period of the planet is proportional to the orbit’s size. The cube of the mean distance of a planet from the Sun is proportional to the square of its orbital period T. r³/T²=constant

Different Cases of Projection:

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.

• Orbital Velocity

Definition

The orbital velocity of a satellite is the horizontal velocity with which it must be propelled from a point above the earth's surface in order to circle in a circular orbit around the earth.

An Expression for the Critical Velocity of a Satellite Revolving Around the Earth

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 ve. 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

where Mis the mass of the earth and Gis the constant of gravitation.

For circular motion,

Centrifugal force = Centripetal force

• Gravitational Field

The space that surrounds any mass is known as a gravitational field. Any additional mass brought into this space is subjected to gravitational attraction. In a word, the area in which any mass field of gravity experiences a gravitational pull.

• Gravitational Potential

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.

1. At a distance r from a point mass M, the gravitational potential (V) is given by:

2. The potential energy of a unit mass is converted from the work done on it. As a result, the gravitational potential at any point equals the potential energy of a unit mass positioned there.

3. The gravitational potential energy (P.E.) of a small point mass m put in a gravitational field at a position where the gravitational potential is V is given by

• 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.

2. Kinetic Energy (K.E.):

The Revolution of satellites around circular orbit is having critical velocity (v_c). Hence its kinetic energy is given by:

3. Total Energy (T.E.):

4. Binding Energy (B.E.)

T.E. = -(B.E.)

• Escape Velocity of a Body

Condition: The body is at rest on Earth’s surface, Escape velocity is:

The escape velocity is the smallest velocity at which a body can be launched from the earth's surface and yet escape the planet's gravitational field.

As a result, if a body or a satellite is given the escape velocity, its projection kinetic energy equals its binding energy.

Kinetic Energy of projection = Binding Energy

• Weightlessness

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 exerts 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.)

• Gravity

Gravity is the force of attraction exerted by the earth on a body lying on or near the earth's surface towards its centre. Gravity, often known as the earth's gravitational force, is a type of gravity.

The force of attraction exerted by the earth on the body towards its centre is defined as its weight. Gravitational pull or weight has the same units and measurements as a force.

Significance of NCERT Class 11 Physics Chapter 8 Notes

The NCERT Physics class 11 chapter 8 notes pdf help students thoroughly review the Gravitation chapter and understand its primary concepts. These Gravitation class 11 notes are invaluable not only for board exams, but also for competitive exams such as VITEEE, BITSAT, JEE Main, NEET, and others, because they thoroughly cover the key concepts outlined in the CBSE physics syllabus. Furthermore, the fact that these cbse class 11 physics ch 8 notes are available in PDF format allows students to study offline at any time and from any location.

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