1. Introduction

Introduction

→ Gravitational Force of Earth: If we release a small stone without pushing it from a height, it

accelerates towards earth. Earth attracts everything towards it by an unseen force of attraction. This force of attraction is known as gravitation or gravitational pull

Universal Law of Gravitation

→ Sir Isaac Newton in 1687 proposed a law about the force of attraction between the

objects in the universe which is known as Newton’s law of gravitation.

According to Universal law of Gravitation

→ Every mass in this universe attracts every other mass with a force which is directly proportional to

the product of two masses and inversely proportional to the square of the distance between them

• Let masses (M) and (m) of two objects are distance (d) apart, then force of attraction (F) between

them

F  ∝ M×m

F  ∝ 1/d²

F ∝ Mm/d²

F = (GMm)/d²

where,

G is a constant and is known as Gravitational constant.

Value of G = 6.67×10^-11 Nm²/kg²

G is called universal gravitational constant.

→ If unit of F is in Newton, m is in kg, d is in mere, then unit of G can be calculated as :

G = (F×d²)/Mm, therefor unit will be Nm²/kg²

^{Importance of universal law of gravitation}

^{(i) The force that binds us to the earth.}

^{(ii) The motion of moon around the earth.}

^{(iii) The motion of earth around the sun.}

^{(iv) The tides due to moon and the sun.}

Chapter 10

Gravitation

 

Introduction

Gravitational force of Earth: 

• If we release a small stone without pushing it from a height it accelerates towards Earth. The stone is when accelerated towards earth, means some force is acting on it.
• The force which pulls the object towards the centre of earth is known as gravitational force of the earth. Here, stone also attracts the earth.
• It means every object in universe attracts every other object.
• When a body undergoes circular motion, it experiences a force that acts towards the centre of the circle. This centre-seeking force is called a centripetal force.

Universal Law of Gravitation

• According to the universal law of gravitation, every object attracts every other object with a force.
• This force is directly proportional to the product of their masses.
• This force is inversely proportional to the square of distances between them.

 

 

 

 

 

 

From the above equation we can rewrite them as the following:

  If we remove the proportionality, we get proportionality constant G as the following:

 

 According to, Newton’s universal Law of gravitation

 G = Fr²/ m₁ m₂

SI Unit: Nm² kg^-2

Value of G = 6.673 × 10^-11 Nm² kg^-2 

The proportionality constant G is also known as the Universal Gravitational Constant.

 

Importance of universal law of gravitation
It explains:

• the force that binds us to the earth.
• the motion of moon around the earth
• the motion of planets around the sun.
• the tides due to the moon and the sun.