Gravitational force is the force of attraction by which a body is attracted towards the center of the earth or any other havenly bodies if the body is on or near the surface.
Its SI unit is Newton (N).
Newton's law of gravitation states that "Everybody in the universe attracts every other body with the force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers".
So, F ∝ m_{1}m_{2 } .......... relation 1
F ∝ 1/d^{2}_{ } .......... relation 2
From relation 1 and 2:
F ∝ ( m_{1}m_{2} )/d^{2}F = G . ( m_{1}m_{2} )/d^{2}
Where G is gravitational constant as a proportional constant.
a. Universal gravitational constant:
G is defined as the force of attraction between two bodies of mass 1 kg each kept at a distance of 1 m apart from their centers.
b. Gravitational field:
The gravitational field is the field around any body or heavenly body where the force of attraction by that body is experienced.
c. Acceleration due to gravity:
Acceleration produced on a freely falling body due to the influence of gravity is called acceleration due to gravity.
d. Freefall:
When a body is falling freely under the effect of gravity only, it is called freefall.
e. Weightlessness:
When any body is falling freely, the weight of the body becomes zero which is called weightlessness.
a. Gravitational constant (G) and acceleration due to gravity (g)
G | g |
It is the force of attraction between 2 bodies of mass 1 kg each kept at the distance of 1m between their centers. | It is the acceleration produced on freely falling bodies due to the influence of gravity. |
It is a constant value. | It is a variable value. |
Its unit is Nm^{2}/kg^{2}. | Its unit is m/s^{2}. |
b. Gravity and gravitational force.
Gravity | Gravitational force |
It is the force of attraction by which any body is attracted toward the center of any heavenly body from its surface. | It is the force of attraction by which the two different heavenly bodies are attracted to each other with a certain force. |
c. Gravity and acceleration due to gravity.
Gravity | Acceleration due to gravity |
It is the force of attraction by which any body is attracted toward the center of any heavenly body from its surface. | It the acceleration produced on a freely falling body due to the influence of gravity of any heavenly body. |
d. Mass and weight.
Mass | Weight |
The total amount of matter contained in any body is called mass. | The gravity acting on any body of a certain mass is called weight. |
It depends upon the size and number of atoms present in the body. | It depends upon the mass and value of acceleration due to gravity. |
Its SI unit is Kg. | Its SI unit is Newton (N). |
e. Freefall and Weightlessness.
Freefall | Weightlessness |
When a body is falling freely under the influence of gravity only, it is called freefall. | It is the state of any body having zero weight. |
It is one of the causes of weightlessness. | It is one of the effects of freefall. |
The force of attraction of any heavenly bodies by which any bodies on its surface is attracted towards its center is called gravity. Its SI unit is Newton (N).
Any three effects of gravity are:
Let us consider a body of mass 'm' falling towards the center of any heavenly body of mass 'M' and radius 'R' with the acceleration due to gravity 'g'.
So, force of attraction = (G.M.m)/R^{2}
or, mg = (G.M.m)/R^{2}
or, g = (G.M)/R^{2}
Hence, g produced in any body falling freely has no effects by its mass.
The gravity of any planets depends on the following factors:
M --> Mass of the planet.
m --> Mass of other body experiencing gravity.
R --> Radius of the planet.
The gravity of any heavenly body makes the other objects move around the edge of its gravitational field in a circular path. In this way, any body can be kept moving around the circular path.
The acceleration due to the gravity of a planet is 9.8 ms^{-2} means that the velocity of any body freely falling from any height towards the surface of the planet is increasing by 9.8 ms^{-1} in every second.
As we all know, the parachute prevents accidents while jumping from height by balancing the velocity of the jumping or falling body. It can balance the velocity of any falling body due to the upthrust produced by the atmosphere. But there is no atmosphere on the moon. So, the velocity of our body would be the same as jumping without a parachute. So, we would get an equal injury.
In the experiment, the 'g' of a feather and coin is not the same in the atmosphere but it is the same in a vacuum. In the atmosphere, feathers get accelerated slowly because of the upthrust of the air. However, in space or vacuum, there are no barriers. So, what is conclude is the 'g' in any body is not affected by the mass of the falling body.
When a body is falling freely under the influence of gravity only, it is called freefall.
The conditions for freefall are:
As we all know that, parachutes prevent accidents while jumping from the height by balancing its velocity or not letting it fall freely. It can balance the velocity of the falling body due to the upthrust of an atmosphere. There is a presence of an atmosphere on the earth's surface but not on the moon's surface. So, it doesn't have any effect while falling on the surface of the moon. Hence, we can fall freely on the moon's surface even with a parachute but not on the earth's surface.
We all know that the sun revolves around the sun in the elliptical orbit which is oval in shape.
We also know that the gravitational force between different heavenly bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In position 'A', the distance is shorter; so the gravitational force is higher but in position 'B', the distance is longer; so the gravitational force is less than that in position 'A'.
The state of a body having zero weight is called weightlessness.
The conditions for weightlessness are:
As we all know that, each and every body in the universe is attraction each other according to Newton's law of gravitation. But not only a body is affected by the gravitational force of a single body but also it is affected by several other forces which get balanced. So, two bodies on the surface of the earth don't move towards each other.
We all know that,
g = (G.M)/R^{2}
g ∝ 1/R^{2}
From this, we conclude g is inversely proportional to the square of the radius of any heavenly body. In the equator, the radius is longer than that in the pole. The longer the radius, the less g. So, there is a higher g at the pole than that in at the equator.
So, the weight of any body will increase, if it is taken from equator to pole becasue we have W = mg where mass remenins constant.
We all know that,
g = (G.M)/R^{2}
g ∝ 1/R^{2}
From this, we conclude g is inversely proportional to the square of the radius of any heavenly body. In the equator, the radius is longer than in the pole. If the radius decreases, the g increases. So, there is a higher g in the pole than at the equator. Therefore, the body will fall faster in pole if it is dropped from equal height at the equator and the pole.
Newton's law of gravitation states that the force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It is the law that is valid and practical in the whole universe.
So, Newton's law of gravitation is a universal law.
We all know that G is the force of attraction between 2 bodies each of mass 1 kg and kept at a distance of 1m between their centers. It is a constant value that is measured in a vacuum and is the same in the whole universe. So, G is a universal gravitational constant.
As we all know that 'g' is inversely proportional to the square of the radius of the earth.
Here, g ∝ 1/R^{2}
We all know that, g ∝ 1/R^{2}
From this, we conclude g is inversely proportional to the square of the radius of any heavenly body. If the radius increases, the 'g' will decrease.
Though the mass of Jupiter is very high, its volume is also very high that results in a higher radius. So, the 'g' of Jupiter gets its value decreased. Hence, the mass of Jupiter is significantly high than that of the earth but the 'g' varies a little only.
The value of acceleration due to gravity 'g' is inversely proportional to the square of the radius of any heavenly body.
Here, g ∝ 1/(R+h)^{2} where h is the height of surface from R.
So, if the height increases, the 'g' will decrease. There is more height in the mountain than that in Terai. So, 'g' is higher in Terai than in the mountaions.
From, W = mg
W ∝ g
So, W is higher in Terai than in the mountains.
We all know that,
W = mg
W ∝ m since g is constant on the same surface.
So, if the mass is more, more force should be applied to overcome its weight.
Therefore, it is difficult to lift a big stone than a smaller one on the earth's surface.
During the fall, the folded paper experiences less upthrust of the atmosphere than that by unfolded one. So, the folded paper gets accelerated faster than the unfolded one and eventually strikes the ground faster.
As we all know that the parachute prevents accidents while jumping from height by balancing the velocity of the jumping or falling body. It balances the velocity of the body due to the influence of upthrust given by the atmosphere. But, there is no atmosphere on the moon's surface through the earth's surface has. So, parachutists are not hurt on the earth's surface but get hurt on the moon's surface.
Any 4 limitations of balanced chemical eqn are:
The universal force of attraction acting between all matter is called gravitation. The factors that affect gravitation are only mass and distance. Its SI unit is Newton's per Kilogram.
Newton's law of gravitation is usually stated as that every particle in the universe has a force directly proportional to the product of their masses and inversely proportional to the distance between their centres.
Universal constant 'G' can be defined as the force of gravitational product between two bodies of unit mass each, separated by the unit distance between their centres. The SI unit of G is Nm^{2}kg^{-2}. Its value is 6.67*10^{-11}Nm^{2}kg^{-2}.
Both coin and feather will reach the ground at the same time because air resistance is the only hindrance an object may suffer through falling.
A body weighs more at the poles than in the equator because the gravitation is more at the poles than in the equator.
When the masses of two objects is doubled, then the gravity between them is quadrupled; and so on. Since the gravitational force is directly proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitation forces.
The sense of weightlessness in orbiting satellites is because of the lack of any contact forces. The only force that acts upon humans in space is the force of gravity, which acts at a distance; but as there is no counter-force, we do not experience the sensation of weight over there. The counter or force-of-contact is missing because everything that floats in space does so due to the acceleration due to gravity being the same. Thus, both the astronaut and the satellite have the same value of g, which is again equal to the centripetal acceleration of the satellite. These two neutralize each other, causing everything to appear weightless.
The importance of gravity force are as follows: