1. Introduction

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/ mm2

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.

 

 

 

 

2. Gravitational Constant and its Units

Freefall
•    When an object falls down towards the earth under the gravitational force alone, we say the object is in free fall.
•    The velocity of a freely falling body changes and is said to be accelerated.
•    This acceleration is called acceleration due to gravity, denoted by ’g’. Unit is m/s2.
•    The motion of objects under the influence of gravity ‘g’ does not depend on the mass of the body. All objects fall at the same rate.
We know that, F= ma
Therefore, F = mg
The force (F) of gravitational attraction on a body of mass m due to earth of mass M and radius R is given by

 

 

g.    But the acceleration due to gravity is represented by the symbol g. Therefore, we can write
h.    F = mg               ... (2)
i.    From the equation (1) and (2), we get

 

 

j.    When body is at a distance ‘r’ from the centre of the earth then

 

 

 

 

 

 

 

 

 

Weight of object on the moon
Just like the Earth, the Moon also exerts a force upon objects. Hence, objects on moon also have some weight. The weight will not be same as than on the earth. So, weight on the Moon can be calculated as -


 

 

 

 

 

 

 

 

 

3. Weight and Mass

Mass:

•    Mass of an object is the measure of its inertia. 
•    It is the matter present in it. It remains the same everywhere in the universe.
Weight:

•    The force of attraction of the earth on the object is known as the weight of the object. 
•    It’s S.I. unit is Newton.
W = m x g
Thrust:

•    The force that acts in the perpendicular direction is called thrust.
•    It is similar to force applied to an object
•    It is a vector quantity.

Pressure

•    The force that acts per unit area of the object is pressure.
•    It is the thrust per unit area.
•    Pressure is denoted by ‘P'
•    P = thrust/ area = force/ area = F/A
•    SI unit: N/m2 or Pa (Pascal)

Applications of pressure

•    The base of high buildings is made wider so that weight of the walls act over a large surface area and pressure is less.

•    School bags are having broad strap so that the weight of the school bags fall over a large area of shoulder and produce less pressure and become less painful.

•    All liquids and gases exist pressure in all direction.
 

 

4. Buoyancy and Density

Buoyancy

•    Whenever an object is immersed in a liquid, the liquid exerts a buoyant force or upthrust in the opposite direction of the gravitational force. This is also called the Force of Buoyancy.
•    It depends upon the density of the fluid.
•    Therefore, an object is able to float in water when the gravitational force is less than the buoyant force.
•    Similarly, an object sinks into the water when the gravitational force is larger than the buoyant force.

Archimedes principle

•    According to the Archimedes principle, whenever an object is immersed in a liquid (fully or partially), the liquid exerts an upward force upon the object. The amount of that force is equivalent to the weight of the liquid displaced by the object.

Why does an object sink or float on water?

•    An object can sink or float on water based on its density with respect to water. The density is defined as mass per unit volume.
•    Objects having a density less than water float in it. For Example, Cork flows in water because its density is lower than that of water.
•    Objects that have a density higher than water sink in it. For Example, Iron nail sinks in water because the density of iron is more than water's density.

Thus, we can conclude that buoyancy depends upon:

The density of the liquid
The volume of the object (as the volume of object increases, its density decreases and vice-versa

Application of Archimedes Principle:

•    In evaluating relative density
•    In designing ships and submarines
•    In making lactometers and hydrometers

Relative Density

 

 

 

 

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