### FORCE

#### Force:

A force is a physical quantity which causes or tends to cause a motion in an object at rest or changes or tends to change the direction of motion of a moving object or the shape or size of the object. The SI unit of force is Newton (N) while its CGS unit is dyne (1N=105 dyne).

#### Gravitation:

All the objects in the universe attract each other with a force, which is called gravitation.

#### Gravitational Force:

The magnitude of force of attraction between any two bodies in the universe is called gravitational force. Its symbol is F and SI unit is Newton (N).

#### Consequences of gravitational force:

i) Tides in seas and oceans are due to the gravitational force of the sun and moon.

ii) The planets revolve around the sun due to the presence of gravitational force.

iii) Existences of solar system and galaxies.

iv) Rainfall and snow fall is possible only due to gravitational force of the earth.

v) Artificial and natural satellites revolve around the earth due to the gravitational force between the earth and the satellite.

#### Affecting factors for gravitational force:

i) The product of mass of object i.e., F ∝ M1M2

ii) The square distance between the centres of body i.e., F ∝ 1/d2

#### Newton law of gravitational:

Newton’s universal law of gravitation states that, “The gravitational force produced between any two bodies of the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.”

#### Applications of Newton’s Universal law of Gravitation:

i) This law helps to determine the mass of the earth, moon, sun and other heavenly bodies.

ii) This law helps to determine the distance between bodies existing in the universe.

iii) This law helps in discovering new planets, stars and other heavenly bodies.

iv) It is used to study the binary stars.

#### Verification of Newton’s law:

Consider the two bodies of the mass M and M with force F acting between them towards their centre. If the distance between their centers is d then,

According to Newton’s universal law of gravitation,

We have F ∝ M1M2 —1

F ∝ 1/d2 —2

Combining 1 and 2 we get, F ∝ M1M2/d2

F=GM1M2/d2

Where G is proportionality constant which is known as universal gravitational constant.

The numerical value of gravitational constant (G) is 6.67*10-11 and its unit is Nm2/Kg2

#### Gravitational constant ‘G’:

The force of attraction between two bodies having mass 1 kg of each separated by distance 1 m taken from their centre’s is called gravitational constant. Its value is equal to 6.67×10-11 Nm2/kg2 and SI unit is Nm/kg. Its value was calculated by Henry Cavendish by using a sensitive balance called the Torsion balance in 1798 AD.

#### Conditions for Gravitational force ‘F being equal to Gravitational constant ‘G’:

The gravitational force ‘F’ exerted between two bodies having mass 1 kg each, separated by distance 1m taken from their centers is equal to gravitational constants ‘G’.

#### Properties of Gravitational constant (G) that makes it universal:

i) The value of ‘G’ is independent of the nature and chemical composition of the masses of bodies.

ii) The value of ‘G’ is independent of the medium (denser or rarer) in which the bodies are kept.

iii) The value of ‘G’ is independent of physical factors like state of object, temperature, pressure, etc.

#### Null point:

The space between the two heavenly bodies at which the resultant gravity is zero, is called null point.

#### Gravity:

The force of attraction with which a planet, satellite or star pulls a body towards its centre is called gravity. Its SI unit is Newton (N).

#### Effects of gravity:

i) Acceleration is produced on freely falling body.

ii) Everybody has some weight.

iii) The earth is surrounded by the atmosphere. Acceleration is produced on freely falling body.

iv) We can stand and walk on the surface of the earth.

v) All the objects like buildings, bridges, etc. can stand on earth’s surface and rivers flow from high level to low level.

vi) Every objects falls towards the surface from a certain height.

#### Affecting factors for gravity:

i) Mass of planet or satellite (M): Gravity is directly proportional to mass of planet or satellite i.e., F ∝ M.

ii) Radius of planet or satellite (R) : Gravity is inversely proportional to radius of planet or satellite i.e., F ∝ 1/R2.

#### Gravitational field:

The space around the heavenly body (planet or satellite) up to where it can exert gravitational force on other masses is called gravitational field. Theoretically, the gravitational field extends up to infinity.

#### Gravitational field intensity (I):

The gravitational field intensity at a point on space around a heavenly body (planet or satellite) is defined as the gravitational force experienced by an object of unit mass placed at that point. It is denoted by ‘I’ and its SI unit is N/kg.

#### Acceleration due to gravity:

The acceleration produced in a freely falling body due to the force of gravity of the earth is called acceleration due to gravity. It is denoted by ‘g’ and its SI unit is m/s2.

#### The relation between radius (R) and acceleration due to gravity (g) :

The acceleration due to gravity is inversely proportional to the square of the radius of planet or satellite.

g ∝ 1/R2

#### Verification of Relation between acceleration due to gravity and radius of the earth:

Let M be the mass and R be the radius of the earth and m be the mass of the body kept at the surface of the earth,

According to the Newton’s law of gravitation the force of attraction between them is given by,

F=G Mm/R2 —1

Also the body is attracted towards the centre of the earth with a force given by,

F=mg —2

From 1 and 2, mg = G Mm/R2

g=GM/R2 —3

G and M are constant whereas R varies because radius of the earth is more at the equator than at poles.

From 3,

We can say that the acceleration due to the gravity is independent to the mass of the body but depends on the mass and radius of the earth.

Variation of the value of g:

a. Variation due to the shape of the earth: g ∝ 1/R2

Value of the g maximum at poles but minimum at equator.

b. Variation due to the height from the surface of the earth: g’ = (R/R+h)2g

If we increase the height from the surface of the earth the quantity in the bracket becomes less than 1. And the acceleration due to the gravity decreases as height from the surface is increased.

c. Variation from the depth of earth surface: g’ = g(R-x)/R since the quantity (R-x)/R is less than 1 .The value of g insidethe earth decreases with increase in depth.

At centre of the earth x=R so gravity at the centre of the earth is 0.

#### Factors upon which acceleration due to gravity depend:

i) Mass of planet or satellite (M).

ii) Radius of planet or satellite (R).

#### Mass:

Total quantity of matter present in any object is called mass. Mass of an object depends on total number of atoms (particles) and average mass of atom. Mass of an object does not change anywhere on the earth, in the space, or on any planets. The SI unit of mass is kilogram (kg).

#### Weight:

The force with which the earth attracts any object on its surface towards its centre is known as weight. Its SI unit is Newton (N). Spring balance measures the weight of an object. Weight of an object differs from place to place because of the difference in the value of ‘g’ form place to place.

#### Free fall:

If an object is falling with the acceleration of acceleration due to gravity in the absence of air resistance is called free fall. The acceleration produced on an object during the free fall is equal to the acceleration due to gravity at that place. There is no perfect free fall of the object falling on the earth due to air resistance. The surface of the moon is not covered by the air. So, the falling of any object on it is free fall.

#### Weightlessness:

The weight of an object falling freely under the effect of gravity appears to be zero. It is called weightlessness.

#### Conditions for weightlessness:

i) When a body is falling freely, it becomes weightlessness.

ii) When a body is in the space at null point.

iii) The body in the rocket (artificial satellite) becomes weightlessness when the rocket (artificial satellite) is orbiting around a heavenly body.

#### Conclusion of Feather and Coin experiment:

The acceleration produced due to gravity in all object will be the same at a particular place for all, if there is no any external resistance.