## Introduction

#### What is Gravitational Force?

Every object in the universe is attracting every other object of the universe. The force of attraction between any two objects in the universe is known as the “force of gravitation”.

Gravitational force is a weak force and cannot be observed unless large masses are involved. However, it is a long-range force.

According to Newton’s law of gravitation, the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If m1 and m2 be masses of two objects separated by a distance d, the gravitational force of attraction between them is given by

The universal constant of gravitation G is numerically equal to the force of attraction between two objects of unit mass each separated by unit distance.

G is called a universal constant because its value does not depend on the nature of intervening medium or temperature or any other physical variable. As value of G is extremely small, the gravitational force between ordinary terrestrial objects is so small that it cannot be detected. However, force of attraction acting on an object due to earth, force of attraction between earth and the moon, force experienced by planets due to gravitational attraction of sun can be easily felt and measured.

#### How does the moon orbit the earth?

Moon is revolving around the earth in a circular orbit. Circular motion is an accelerated motion because here direction of motion is continuously changing from point to point. Hence, in accordance with Newton’s second law of motion, a force is needed for circular motion. This force is known as ‘centripetal force’. Centripetal force is a force needed to keep an object moving along the circular path and the force always acts towards the centre of circle.

In case of circular motion of moon around the earth, the centripetal force is provided by gravitational attraction of earth on moon. Similarly centripetal force needed for circular motion of planets around the sun is provided by gravitational attraction force due to sun on the planet.

#### What is the force of gravity due to earth?

The force of gravitational attraction exerted by the earth on an object is called the “force of gravity’'. Force of gravity acting on an object of mass m situated on earth’s surface or near it is given by

where M = mass of earth and R = radius of earth.

#### What is acceleration due to gravity?

The acceleration produced in a freely falling object on account of the force of gravity is known as the acceleration due to gravity. It is denoted by symbol ‘g’.

The value of acceleration due to gravity on the surface of earth is given by

The mean value of g on the surface of earth is found to be 9.8 ms-2.

Value of g varies from place to place. On surface of earth value of g is more at poles than at the equator. Again value of g decreases as one goes away and away from the earth.

#### When do we say that an object is under free fall?

When an object falls towards the earth under the force of gravity alone, we say that the object is in free fall. A freely falling object experiences a constant acceleration of g (=9.8ms-2) during its downward motion. However, if an object is projected vertically upward with a certain velocity, its velocity goes on decreasing due to gravity, till it comes to rest and then starts falling vertically downward under gravity.

#### How do the 3 equations of motion change under gravitation force?

The three equations of motion viz,

(i) v = u + at,

(ii) s = ut + 1/2 at2, and

(iii) v2 - u2 = 2

as are true for motion of objects under gravity.

For free fall, the value of acceleration a = g = 9.8ms-2.

If an object is just let fall from a height then in that case u = 0 and a = +g = +9.8ms-2.

If an object is projected vertically upwards with an initial velocity u, then a = -g = -9.8ms-2 and the object will go to a maximum height h where its final velocity becomes zero (i.e.. v = 0). In such a case

### What is Mass?

The mass of an object is a measure of its inertia. Mass of an object is constant and does not change from place to place.

### What is Weight?

The weight of an object is the force with which it is attracted towards the earth. Weight W of an object of mass m will be W = mg.

Weight is a force acting vertically downwards. It means that it is a vector. As weight of an object is a force, its SI unit is newton (N). An object of mass m = 1 kg has thus a weight of W = 1 x 9.8 = 9.8 N.

At a given place weight of an object is directly proportional to its mass i.e.,

(at a given place). Due to this reason at a given place, we may use the weight of an object as a measure of its mass.

#### What is the difference between Mass and Weight?

Mass of an object remains the same everywhere but weight of an object changes from place to place. For an object of mass m weight W is dependent on value of g.

Force of gravity due to moon is 1/6th of the force of gravity due to earth.

Hence, due to this very reason weight of an object on moon will be 1/6th of its weight on the earth.

#### What is Thrust?

The normal force acting on a surface, due to weight of an object placed on the surface, is called ‘thrust’. As thrust is a sort of force hence its SI unit is “a newton” (N).

The thrust on unit surface area is called pressure.

Thus, pressure on a given object is the normal force acting on its surface per unit surface area.

SI unit of pressure is N m-2 but it is also called pascal and denoted by symbol Pa. ∴ 1 pascal (1 Pa) = 1 N m-2

#### How does pressure vary with area?

Same force acting on a smaller area exerts a larger pressure. It is due to this reason that a nail or a pin has a pointed tip and knives have sharp edges.

Given force acting on a larger area exerts a smaller pressure. It is due to this reason that foundations of houses are made broad, base of dams is made broad, sleepers are laid below the railway line and so on.

#### What is a fluid?

A fluid is that state of matter which can flow. All liquids and gases are fluids. As fluids have weight, they exert pressure on the base and the walls of the container in which they are kept.

In a fluid, pressure applied at any one place is transmitted equally in all directions.

#### What is Buoyant Force?

Whenever an object is immersed in a fluid, it experiences a force in the vertically upward direction due to that fluid. This force due to a fluid acting in upward direction is called ‘force of buoyancy’ or ‘buoyant force or up thrust. Magnitude of force of buoyancy acting on an object depends upon

(i) the volume of an object immersed into the fluid, and

(ii) the density of the fluid.

Due to force of buoyancy the net weight of an object becomes less than its normal weight.

Archimedes Principle: A Greek scientist Archimedes discovered a principle regarding buoyant force (or the loss in weight of an object when immersed in a fluid). According to Archimedes’ principle “whenever an object is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it”.

Alternately, according to Archimedes’ principle “there is always a loss (decrease) in weight of an object when it is immersed fully or partially in a fluid and the loss in weight is equal to the weight of the fluid displaced by the immersed part of given object”.

Applications of Archimedes Principle:

Archimedes’ principle has many applications. Design of ships, submarines, lactometer and hydrometer are some of the applications of Archimedes’ principle.

#### What is Density?

Density of a substance is defined as its mass per unit volume. Its SI unit is kg m-3. However, sometimes unit g cm-3 is also used for density. It is found that 1 g cm-3 = 1000 kg m-3.

Relative density of a substance is the ratio of its density to the density of water.

Relative density is a unit-less quantity.

We know that an iron nail immersed in water sinks but a wooden piece remains floating on water. It is found that objects having density less than that of the liquid, in which they are immersed, float on the surface of fluid. On the other hand, if density of the object is more than the density of the fluid in which it is immersed then the object will sink in that fluid.

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