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M.E.S INDIAN SCHOOL, DOHA -QATARNotes 2022 - 2023
Section : Boys & Girls Date : 25-09-2022
Class & Div. : XI (All divisions) Subject: Physics
Lesson / Topic: Gravitation
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GRAVITATION
Ptolemy introduced the ‘geocentric’ model to explain the motion of planets.
Copernicus put forward the ‘heliocentric theory’ in which the sun is at the centre of the planetary
system.
UNIVERSAL LAW OF GRAVITATION
Every body in the universe attracts every other body with a force which is directly proportional to the
product of their masses and inversely proportional to the square of the distance between them.
Consider two bodies of masses m1 and m2 with their centres separated by a distance r. The gravitational
force between them is,
m1 m2
Fα
r2
𝒎𝟏 𝒎𝟐
F =G
𝒓𝟐
where G is the universal gravitational constant.
Hence, the Gravitational constant ‘G’ is numerically equal to the gravitational force of attraction between
two bodies of mass 1 kg each separated by a distance of 1 m.
Then,
F r2 [MLT−2 ] [L2 ]
G= = [M2 ]
= [M−1L3 T −2]
m1 m2
The value of G is 6.67 × 10−11 N m2 kg−2 and its dimensional formula is M−1 L3 T−2.
Newton’s law of gravitation in vector form.
Consider two point objects of masses m1 and m2 seperated by a distance r. The mass m2 is attracted by
mass m1 with a gravitational force ⃗⃗⃗⃗⃗⃗
𝐹21 is given by,
F 061, Rev 01, dtd10th March 2020
1
, 𝑚1 𝑚2
⃗⃗⃗⃗⃗
𝐹21 = G 21…………………(1)
𝑟̂
𝑟2
Where 𝑟̂ ⃗⃗⃗⃗⃗⃗
21 is the unit vector in the direction of 𝐹21
Similarly,
The mass m1 is attracted by mass m2 with a gravitational force ⃗⃗⃗⃗⃗
𝐹12 is given by,
𝑚1 𝑚2
⃗⃗⃗⃗⃗
𝐹12 = G 12…………………(2)
𝑟̂
𝑟2
Where 𝑟̂ ⃗⃗⃗⃗⃗
12 is the unit vector in the direction of 𝐹12
But, 𝑟̂
12 = - 𝑟̂
21
Then eqn (1) becomes,
𝑚1 𝑚2
⃗⃗⃗⃗⃗
𝐹21 = - G 12…………………(3)
𝑟̂
𝑟2
From eqn (2) & eqn (3)
⃗⃗⃗⃗⃗
𝐹12 = - ⃗⃗⃗⃗⃗
𝐹21
i.e., Newton’s Law of Gravitation obeys Newton’s third Law of motion.
Characteristics of Gravitational force
1. It is always attractive.
2. It is independent of the intervening medium.
3. It is a central force.
4. It is a conservative force.
5. It is the weakest force in nature.
6. It is a long range force.
Acceleration due to Gravity of Earth
The acceleration with which a body falls towards the surface of earth when dropped from a height is called
acceleration due to gravity. Or, it is the acceleration of a freely falling body.
Acceleration due to gravity near the surface of earth, g = 9.8 m/s2
Expression for acceleration due to gravity
Consider a body of mass ‘m’placed on the surface of earth. The gravitational force on the body is given by
𝐺𝑀𝑚
F= …………………………..(1)
𝑅2
Again w e have,
F = m g………………………………..(2)
From eqn (1) & eqn (2)
𝐺𝑀𝑚
mg =
𝑅2
th
F 061, Rev 01, dtd10 March 2020
2
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