JEE Main Gravitation Revision Notes - PDF Download
From the Latin word gravitas, the term Gravity has been derived, which means gravitation or 'weight', and it is defined as a natural phenomenon by which all things with energy or mass—including planets, galaxies, stars, and even light—are brought toward or gravitate toward one another. On planet Earth, gravity provides weight to physical objects, and the gravity of the moon causes the ocean tides. The attraction of gravitation of the original gaseous matter present in the Universe causes it to begin coalescing and forming stars and causes the stars to group together into galaxies.
So gravity is responsible for many things such as large-scale structures in the Universe. Gravity has a huge effect, although its effects become increasingly weaker as objects get far away. In 1915, gravity was most accurately described by the general theory of relativity which was proposed by Albert Einstein, which describes gravity not as a force, but as a consequence of spacetime curvature due to the uneven distribution of mass. One of the most extreme examples of this curvature of spacetime is a black hole, from which not even a single ray of light can escape once past the black hole's even horizon. For most applications, however, gravity is very well approximated by Newton's law of gravity, which clearly describes that gravity is a force, which causes any two bodies to be attracted to one another. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
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Important topics to be studied in Gravitation Chapter
Here are the important topics:
Kepler’s first law (law of elliptical orbit):
A planet moves around the sun in an elliptical orbit with the sun situated at one of its foci.
Kepler’s second law (law of areal velocities):
A planet moves around the sun in such a way that its areal velocity is constant.
Kepler’s third law (law of time period):
A planet moves around the sun in such a way that the square of its period is proportional to the cube of the semi-major axis of its elliptical orbit.
Law of gravitation by Newton:-
Every particle of matter attracts every other particle with a force that varies directly as the product of masses of two particles and inversely as the square of the distance between them in this universe .
Formula of dimensional of G:G = Fr2/Mm =[MLT-2][L2]/[M2] = [M-1L3T-2]
Gravity from acceleration (g):- g = GM/R2
Variation of g along with altitude:- g' = g(1- 2h/R), if h<<R. Here Radius of the earth is r and h is the height of the body above the surface of the earth.
Variation of g along with depth:- g' = g(1- d/R). Here g' be the value of acceleration due to gravity at the depth d.
Variation with latitude:-
At poles:- θ = 90°, g' = g
At equator:- θ = 0°, g' = g (1-ω2R/g)
Here ω is the angular velocity.
As g = GMe/Re2 , therefore gpole > gequator
Mass of Gravitational:- m = FR2/GM
Field intensity Gravitational:-
E = F/m
Weight:- W= mg
On the earth Gravitational intensity (Es):-
Es = 4/3 (πRρG)
Here R is the radius of the earth, G is the gravitational constant and ρ is the density of earth.
Gravitational potential energy (U):- U = -GMm/r
(a) Two particles: U = -Gm1m2/r
(b) three particles: U = -Gm1m2/r12 – Gm1m3/r13 – Gm2m3/r23
Potential Gravitational (V):- V(r) = -GM/r
On the surface of the earth,
Here R is the radius of the earth.
Escape velocity (ve):-
It is described as the least velocity with which a body has to be be projected vertically upward so that it may just escape the gravitational pull of the earth.
ve = √2GM/R
or, ve = √2gR = √gD
Here R is the radius and D is the diameter of the earth
Scape velocity (ve) in terms of earth’s density:- ve = R√8πGρ/3
Orbital velocity (v0):-
v0 = √GM/r
If a satellite of mass m revolves in a circular orbit around the earth of radius R and h be the height of the satellite above the surface of the earth, then,
r = R+h
So, v0 = √MG/R+h = R√g/R+h
In the case of a satellite, orbiting very close to the surface of the earth, then orbital velocity will be,
v0 = √g
Relation between escape velocity ve and orbital velocity v0:- v0= ve/√2 (if h<<R)
Time period of Satellite:- Time period of a satellite is the time taken by the satellite to complete one revolution around the earth.
T = 2π√(R+h)3/GM = (2π/R)√(R+h)3/g
If h<<R, T = 2π√R/g
Height of satellite:- h = [gR2T2/4π2]1/3 – R
Energy of satellite:-
Kinetic energy, K = ½ mv02 = ½ (GMm/r)
Potential energy, U = - GMm/r
Total energy, E = K+U
= ½ (GMm/r) + (- GMm/r)
= -½ (GMm/r)
Gravitational force in terms of potential energy:- F = – (dU/dR)
Acceleration on moon:-
gm = GMm/Rm2 = 1/6 gearth
Here Mm is the mass of the moon and Rm is the radius of the moon.
Some Simple Tips to Prepare for JEE Mains
Start with finding out the latest syllabus. Bifurcate them subject-wise and class-wise. Check the exam pattern and weightage of every chapter in each subject. Although you need to give equal importance to every topic, write down the percentage weightage and the number of questions that tend to appear from those topics besides the list of chapters in the syllabus.
Your books, especially NCERT books, should be your primary source of study. Study the chapters in and out. Make small notes of the important laws, definitions, and formulae so that you can take a quick glance when you desire.
Once you think you have studied and understood the chapters well, solve questions from previous years and sample papers. Time yourself while solving the questions to keep track of your speed and accuracy.
Take as many mock tests as you can so that you can assess your level of preparedness and discover the areas you need to focus on more. Learn from your mistakes and revise the topics again and again.
Keep sufficient time for revision! This does not just apply to your preparation but also while you are taking the actual JEE Mains exam. Revision is a vital time when you can rectify silly errors and save a lot of marks.
FAQs on JEE Main Gravitation Revision Notes
1. Define Gravitation?
Bodies exert the force of attraction on one another as a result of their masses. An example of a process that is caused by this interaction is falling off a body on the surface of the earth due to the gravitational force. Gravitation or just gravity is the force of attraction found between two bodies. All the objects attract each other with a certain force, but in most cases, the force is weak to be observed owing to the large distance of separation in the universe. Besides, gravity's range is also infinite but the effect gets weaker as objects begin to move away.
2. Explain the Difference Between Gravity and Gravitation.
Though both the terms sound the same they are different terms, gravitation is defined as the force between two bodies on the other hand gravity is defined as force occurring between earth and body.
Nature of force
It may be an attractive force or repulsive force as well.
It is always a kind of attractive force.
The direction of this gravitational force is along the radial direction from the masses.
The direction of this force is along the line joining the earth's center and the center of the body. It is always working towards the center of the earth.
3. At What Height Gravity Ends?
At sea level that is near to the surface of the earth, the gravity decreases by the height such that linear extrapolation gives zero gravity at the height of half of the earth's radius and altitude in meters.
4. Why is Only Gravitational Called as a Universal Law?
his law is called so because it applies to all the bodies having mass. All bodies are governed by the same law that is the law of gravitation by Newton, so it is called the universal law of gravitation. For two masses m1 and m2 placed at a distance d, the gravitational force between them will always be given by: Fg=Gd2m1m2. The core of the law is that everything falls towards everything else. ie. Gravitation happens universally — to everything.
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