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 states that everybody in this universe attracts every other body with a force which is:
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)
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)
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:
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.
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.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
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.
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.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 gravitational force (F) produced between two heavenly bodies is directly proportional tothe product of masses of the two heavenly bodies (m_{1} and m_{2}) and inversely proportional to the square of the distance (d) between them.
i.e.
Gravitational constant is the force of gravitation between two bodies each with a mass of 1kg placed at a distance of 1m apart.
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,
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^{12-13}
=99.99kg.
Hence, the mass of the man is 99.99kg.
Here,
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.
Let,
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.
If the mass of two objects of 1 kg each is kept at a distance of 1m, the value of gravitational force (F) will be 6.67 × 10^{-11} N.
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.
The force of attraction between the bodies and the earth in which earth pulls the bodies towards it's center is called gravity
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 ______.
west
north
east
center of the earth
The value of G is ______.
Gravitational force depends upon ______.
distance between their center of masses only
masses and distance between their centers
none of above option
masses only
SI unit of gravitational constant is ______.
Name the fundamental force which holds the planets in their orbits around the sun.
centrifugal force
frictional force
gravitational force of attraction
centripetal force
The acceleration due to gravity is zero at ______.
at equator
at poles
centre of earth
at the bottom of earth
If acceleration due to gravity on earth is 10 m/s^{2} then, the acceleration due to gravity on moon is ______.
16.6
14.6
1.66
67.6
The acceleration due to gravity of a body moving against gravity is ______.
-10
10
9.8
-9.8
What does the acceleration due to gravity becomes when radius is reduced to half?
Which metal is obtained from bauxite?
gold
iron
boron
almunium
ASK ANY QUESTION ON Gravitation
You must login to reply
Jul 08, 2017
0 Replies
Successfully Posted ...
Please Wait...
Apr 27, 2017
0 Replies
Successfully Posted ...
Please Wait...
Apr 27, 2017
0 Replies
Successfully Posted ...
Please Wait...
ankit
what are the consequences of newtons law of graviation?
Mar 18, 2017
1 Replies
Successfully Posted ...
Please Wait...