GRAVITATION

Gravitation and gravity

• Gravitation is the force of attraction between any two bodies 
• Gravity is the force of attraction between a body and the Earth. It pulls all the objects towards the earth. It holds the stars together.

 Gravitational force- Gravitational force is the force with which earth attracts the other body.

Mass and Weight 

• Mass is the quantity of matter contained in the body.
• Mass is a scalar quantity which has only magnitude but no direction.
• Mass does not change from place to place, it is always remains constant and SI unit of mass is kilogram (kg) and Mass of a body can never be zero
• Weight of the body is the force with which Earth attracts the body. It depends on Mass(m) and gravity (g). Weight of the object becomes zero if g is zero. The SI unit of weight is Newton. The weight of a body is maximum at the pole and minimum at the equator of the earth.

The Law of Gravitation 

According to the law of gravitation, F is directly proportional to the product of two masses of the objects and inversely proportional to the square of the distance between them. 

If M and m are the masses, F is the gravitational force and r is the distance between two objects then'

F ∝  M x m   and F ∝ 1/r²

Therefore, F ∝ Mm/r².

Or  F = G Mm/r²

The value of G remains constant at all the places in the universe and so it a called universal constant. The value of G does not depend on the medium.

• Hence, if the mass of one object is doubled, then the gravitational force will also get doubled, If the masses of both the objects are doubled, the product of masses becomes four times and hence the gravitational force will also become four times the original value.
• If the distance between the objects is reduced to half, then the gravitational force would become four times and if the distance is increased to double, the the gravitational force would become one fourth.

Unit of gravitational constant G is Nm²kg^-2

Importance of The Universal Law of Gravitation

• It binds all the objects and us to the earth.
• It causes tides in seas on earth.
• It causes the motion of the moon around the earth.
• It causes the motion of planets around the Sun.

Factors on which, the strength of gravitational force depends

• Masses of the objects
• Distance between the objects 

Acceleration due to gravity

If an object is moving under the influence of only gravitational force, near the earth the gravitational force produces a uniform acceleration in the objects, which is called acceleration of free fall or acceleration due to gravity. It is denoted by g and its value is 9.8 m/s².

The earth is not a perfect sphere. As the radius of the earth increases from the pole to the equator, the value of g becomes smaller at the equator and greater at the pole.

To calculate the value of 'g'

• According to the Newtons third law of motion, the force of attraction between the earth and the earth and body is given by F = GMm/r²
  Where m = mass of the object, M = mass of the earth, r = distance between earth and object and G =universal constant.
• And according to Newton's second law: F = mg.  (where g is the acceleration due to gravity) Therefore, mg = GMm/r²    and g = GM/r². 
• If the body is located on the earth's surface of the earth then r = R Therefore g = GM/R². This expression gives acceleration due to gravity at the surface of the earth where the value of g is 9.8 m/s²

Factors Affecting the Value of g

• As the radius of the earth increases from the poles to the equator, the value of g increases and greater at the poles than at the equator.
• As the height increases, the value of g decreases.

Motion of Objects Under the Influence of Gravitational Force of the Earth

If an object is falling towards earth with initial velocity u and gravitational acceleration g, and final velocity v after covering the height h in time t, then the three equations of motion can be represented as:

•  v = u + ght
• h = ut + ½gt²
• v² = u² + 2gh

The value of g is  positive when the object is moving towards earth and negative when the object is thrown in opposite direction of the earth.

Weight of the object on the moon

The weight of an object on the moon is one-sixth the weight of the object on the earth as gravitational force of moon is one sixth of earth.