Gravitation
The force of attraction between any two bodies in the universe is called gravitation.
Force is that push or pull which changes or tends to change the state of rest or uniform motion in a straight line.
Newton's law of gravitation
Newton's law of gravitation states that everybody in this universe attracts every other body with a force which is:
 Directly proportional to the product of their masses i.e. F ∝ m_{1}m_{2}...(i) and
 Inversely proportional to the square of distance between their centers i.e ..(ii)
Combining Eqn (i) and (ii), we get
Or,
Where G is the proportionality constant which is known as universal gravitational constant.
Numerically,
G = 6.67 X 10^{11 }
\( \therefore F\; = \; G \frac{m_1\times \;m_2}{d^2}\) .....(iii)
Universal gravitational constant G
The force of gravitation that is exerted between two bodies of unit mass placed at a unit distance from their centers.
i.e. m_{1} =1 kg
m_{2} = 1 kg
d = 1m
Then from Eqn (iii), we get
F= G
Or, F = G
∴G = F
Thus, the gravitational constant 'G' is numerically equal to the gravitational force 'F' when two masses of 1kg are separated by 1meter.
This law is called universal law because this law is applicable to all objects of any size (larger or small) all across the universe (terrestrial or celestial)
Value of G on other planets:
The value of G anywhere in the universe is 6.67 x 10^{11}. It is because G is universal constant and its value remains same everywhere in the universe.
Q: Two objects with a certain masses placed at a certain distance are ones separated by air medium and then by water medium. In which case is gravitational force greater:
A: Since the gravitation force depends upon mass and the distance between masses and does not depend on the medium where two objects are kept, gravitational force is equal in both air and water medium.
Effect on gravitational force of attraction if:
 The masses of both objects is doubled keeping distance constant?
According to the question:
m_{1}= 2m_{1}
m_{2} = 2m_{2}
D = d
∴ New force of attraction(f_{n})
f_{n} = From Eqn iii
Or, f_{n} = 4
Or, f_{n}= 4F
Hence the new force will be 4 times more than the original force.
 The masses of both objects is tripled keeping distance constant
According to the question:
m_{1} = 3m_{1}
m_{2} = 3m_{2}
D = d
∴ new force of attraction
f_{n} = From Eqn (iii)
f_{n} = 9
Or, f_{n} = 9F
Hence the new force will be 9 times more than the original force.  The mass of one body is doubled with distance reduced to half
According to the question:
m_{1} = 2m_{1}
m_{2} = m_{2}
D = d/2
∴ new force of attraction
f_{n} =
Or, f_{n}=
Or, f_{n} = 2 ×4
Or, f_{n} = 8F From Eqn (iii)
Hence the new force will be 8 times more than the original force
 The mass of one body increased fourfold, that of other decreased by onethird with distance increased three times
Let,
Two masses are m_{1} and m_{2}
Distance of separation is d
∴ The mutual force of attraction,
F = ........ (1)
According to the question:
m_{1} = 4m_{1}
m_{2}= 1/3 x m_{2}
D = (3 x d)
∴ new force of attraction
f_{n} = G From Eqn (1)
Or, f_{n} =
Or, f_{n} =
Hence the new force will be 4/27 times less than the original force.
 The masses of both is doubled and distance increased by double?
According to the question:
m_{1} = 2m_{1}m_{2} = 2m_{2}
D = 2d
∴ new force of attraction
f_{n}=
Or, f_{n} =
Or, f_{n} = F from Eqn (1)
Hence the new force will be equal to the original force.
Factors Affecting Gravitational force.
The factors affecting gravitational force are as following:
Since,
F = therefore, the affecting factors are:
Mass of the two bodies' i.e. F∝M_{1}M_{2} when mass increases gravitational force increases.The distance between their centers
i.e. \(F\propto\frac{1}{d^2}\)when the distance increases gravitational force decreases.
 The force of attraction between any two bodies in the universe is called gravitation.
 Newton’s law of gravitation is F=G.\(\frac{M_1M_2}{d^2}\)
 Universal gravitation constant G law is applicable to all objects of any size (larger or small) all across the universe (terrestrial or celestial) F=G.\(\frac{M_1M_2}{d^2}\)
i.e.
Here,
Mass of one body (m_{1})= 10 kg
Mass of second body (m_{2}) = 20 kg
Distance between them (d) = 10 meter
Gravitational force (F)= ?
We have,
or, or,
Here,
Mass of the sun (m_{1}) = 2 × 10^{30}kg
Mass of the earth (m_{2}) = 6 × 10^{24} kg
Distance between the centres of the earth and the sun (d) =1.5 × 10^{11} m
Force of attraction (F)= ?
According to the Newton"s law of Gravitation,
= 6.67 × 10^{11} × = 3.56 × 10 ^{22} N
Hence, the force of attraction between the sun and the earth is 3.56 × 10 ^{22} N.
Given,
Mass of the earth (M)= 6 × 10^{24} kg
Radius of the earth (R) = 6400 km
= 64 × 10^{5} m
= 6.4 × 10^{6} m
Weight of the man (F)= 977 N
Mass of the man (m)= ?
Universal gravitational constant (G) = 6.67 × 10^{11} Nm^{2}/kg^{2}
According to the formula,
or,
= = =999.9510^{1213}
=99.99kg.
Hence, the mass of the man is 99.99kg.
Gravitational force of attraction between two bodies is given by:
When the mass of each body is doubled then new masses will be m_{1} = 2m_{1} and m_{2} = 2m_{2} and distance is tripled, then d = 3d
or, or, or,
The magnitude of the force reduces of the initial force.
Newton"s law of gravitation states that "The force of attraction gravitation between any two bodies in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers".
Solution:
Given,
Distance between the moon and the earth (d) = 3 × 10^{5} km
= 3 × 10^{8} m
Mass of the moon (M) = 7 × 10^{22} kg
Pulling force of the moon (F) = ?
According to the formula,
[G = 6.67 × 10^{11} Nm^{2}/kg^{2}]
=
=
=
= 5.18 × 10^{5} N
Every kilogram of water of river is attracted by 5.18 × 10^{5}N of force of the Moon.
Mass of the first object = m_{1}
Mass of second object = m_{2}
Distance between two objects = d
Force between two objects= F
We have,
……….(i)
Here,
The distance between two objects is doubled,
So, d = 2d
Now, or,
The magnitude of force reduce to of the initial force i.e. force is decreased by 4 times when distance between the objects is doubled.
By calculation,
Mass of the first object (m_{1}) = 1kg
Mass of second object (m_{2})= 1 kg
Distance between two objects (d) = 1 m
Gravitational force (F) = ?
We have,
or,(where, G = 6.67 × 10^{11}Nm^{2}/kg^{2})
=6.67 × 10^{11}N
F =6.67 × 10^{11} N.
We can say that Free fall is the cause and weightlessness is an effect. Similarly Free fall is the condition of body falling freely towards the earth's surface without any external resistance but weightlessness is the condition of having the weight of a body zero.During freefall the weight of the body is zero.
The force of gravity acts on the centre of the earth or any other objects whose gravity acts on other smaller object.

Gravitational force is directed towards ______.
east
north
west
center of the earth

The value of G is ______.
3.37×10^{11}
6.6×10^{11}
6.67×10^{11}
4.4×10^{11}

Gravitational force depends upon ______.
masses and distance between their centers
masses only
distance between their center of masses only
none of above option

SI unit of gravitational constant is ______.
N mkg^{2}
N m^{2}kg^{2}
N m^{2}kg^{2}
N m^{2}s^{4}

If the distance between two bodies is doubled, the force of attraction F between them will be?
1/4F
1/2F
4F
2F

Name the fundamental force which holds the planets in their orbits around the sun.
centripetal force
frictional force
gravitational force of attraction
centrifugal force

The acceleration due to gravity is zero at ______.
at poles
at equator
at the bottom of earth
centre of earth

If acceleration due to gravity on earth is 10 m/s^{2} then, the acceleration due to gravity on moon is ______.
1.66
16.6
14.6
67.6

The acceleration due to gravity of a body moving against gravity is ______.
9.8
9.8
10
10

What does the acceleration due to gravity becomes when radius is reduced to half?
g'=3g
g'=4g
g'=5g
g'=2g

Which metal is obtained from bauxite?
boron
gold
almunium
iron

Why does a dead body floats in water?

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