NCERT Notes for Class 9 Science Chapter: 10 Gravitation

CBSE Class 9 Science notes will assist students in studying the topic thoroughly and clearly.

These CBSE Class 9 Science notes were written by subject experts who made the study material very basic, both in terms of language and format.

## Gravitation

The force of attraction between any two bodies in the universe is defined as Gravitation.

All objects on or near the earth’s surface are attracted (or drawn) toward the earth’s centre. The gravitational force of the earth or gravity of the earth is the force with which the earth pulls things towards its centre.

**UNIVERSAL LAW OF GRAVITATION**

Isaac Newton established the universal law of gravitation.

The attraction force between any two objects in the universe is exactly proportional to the product of their masses and inversely proportional to the square of their distance.

The force is directed along the line connecting the centres of two objects. Consider two bodies A and B with masses m1 and m2, respectively, and whose centres are separated by a

distance D.

The force between two bodies is hence exactly proportional to their mass product.

**F ∝**** m****1****m****2****………(i)**

Because The Force Between Two Bodies Is Equal To The Square Of Their Distance,

**F ∝ ****1****d****2** ……..(ii)

We Get By Combining Eqs. (i) And (ii).

**F ∝ ****m****1****m****2****d****2**** or ****F=G****m****1****m****2****d****2**

where, G=6.67 10-11N-m2/kg2 , is called the universal gravitational constant

Its value is independent of the medium between the two bodies, their masses, or their distance from one another.

If two bodies have weights of 1 kilogramme each and the distance d between

them 1 m, then F = G [∵ m1= m2= 1 kg and d = 1 m ]

Thus, the universal gravitational constant is defined as the gravitational force acting between two objects of equal mass separated by an equal distance in space.

G is denoted by the SI unit** N-****M****2****Kg****-2**. Henry Cavendish (1731-1810) determined the value of G using a sensitive balance

**Importance Of Universal Law Of Gravitation**

Numerous phenomena are effectively described by the universal law of gravitation, as follows:

- The gravitational force that holds us to the earth.
- The moon’s motion around the earth.
- Planets motions around the sun.
- The occurrence of tides is caused by the gravitational force of attraction exerted by the moon.
- The flow of water in rivers is also a result of the earth’s gravitational pull acting on the water.

Newton’s law of gravitation is not applicable in the case of interatomic distances. Because of this reason it cannot be called a universal law any more.

**The Motion Of Moon Around Earth And Centripetal Force**

The force that maintains a body moving in a circular path is referred to as centripetal (centre seeking) force. The centripetal force is responsible for the motion of the moon around the earth.

The centripetal force is provided by the gravitational attraction of the earth, which acts as an attracting force. If there were no such force, the moon would continue to move in a straight line in a uniform fashion.

## Kepler’s Laws of Planetary Motion

In the sixteenth century, Johannes Kepler suggested three laws of planetary motion. The following are the three laws:

**KEPLER’S FIRST LAW**

It claims that the path taken by any planet in its orbit around the sun resembles an ellipse with the sun at one of the foci.

The point in a planet’s orbit closest to the sun is referred to as perihelion, whereas the point farthest from the sun is referred to as aphelion.

**KEPLER’S SECOND LAW**

It states that an imaginary line drawn between the sun and the planet sweeps out equal portions at equal time intervals.

Thus, if the time required for a planet to move from A to B and C to D is equal, the regions AOB and COD are equal.

**KEPLER’S THIRD LAW**

It asserts that the cube of a planet’s mean distance from the sun is equal to the square of the planet’s orbital period T. It is denoted as

r3∝ T2 , r3= K T2

K=r3T2

**T = Time Period Of The Planet (Around The Sun) **

**R = Radius As Mean Distance Of The Planet From The Sun **

**K = Kepler Constant **

Kepler was unable to provide an explanation for the planets’ motions.

Newton showed that the planets move as a result of the gravitational attraction exerted by the sun. Newton calculated the gravitational force of attraction using Kepler’s third law.

Assume that the orbital velocity is v and the orbital radius is r. Then, the force exerted on a planet in orbit is denoted by

**F=****mv****2****r** **……….(i)**

M=Mass Of Planet.

If T Signifies The Duration Of The Time Period, Then

**T=****2****r****v**

**v=****2****r****T** ……….(ii)

Substituting The Value Of V In Eq. (I), We Get

**F=****m****r****(****2****r****T****)****2****=****4****2****m****r****T****2**** ………(iii)**

But According To Kepler’s Third Law Of Planetary Motion,

**r****3****=****KT****2**

**T****2****=****r****3****K**

Putting This Value Into Eq. (Iii), We Get **F=****4****2****mr****(****r****3****K****)****=****4****2****Km****r****2**

Thus, the gravitational force between the sun and the planet is inversely proportional to the square of their respective centres’ distances.

## Free Fall

When objects fall towards the earth only due to the gravitational force of the earth, they are referred to as freely falling objects, and the motion is referred to as free fall.

**Acceleration Due To Gravity (G)**

There is always an acceleration involved when an object is falling towards the earth.

This acceleration is caused by the gravitational pull of the earth and is referred to as acceleration owing to gravity. It is represented by the letter g.

The SI unit for g is identical to the one for acceleration, namely m/s2

let M be the mass of the earth and m be the mass of an object falling freely towards it. The distance between the earth’s and the object’s centres is R.

From newton’s law of gravitation, **F =** **GM****R****2**

Additionally, according to the second law of motion, the force applied on an object, f = ma

since, a = g (acceleration due to gravity )

f = mg

we get from equating RHS of eqs. (i) and (ii)

**mg=****GMm****R****2**** or g=****GM****R****2**

It is from the formula that the acceleration due to gravity is independent of the mass of a falling object. It is entirely dependent on the mass of the earth or other celestial entities.

**Calculation Of The Value Of G**

To calculate value of g, we should put the values of G.M and R in above formula,

g = GM/R2

g = 6.67 x 10-11 N-m2/kg2

m = 6 x 1024 kg

r = 6.4 = 64 x 106 m

putting these values we get, the value of g = 9.8 m/s2

**Equations Of Motion For Free Fall**

The three equations of motion determined before are for bodies experiencing uniform acceleration. When bodies are in free fall, there is a uniform acceleration, i.e. gravity’s acceleration (g) acting downward.

Thus, the following three equations of motion may be used to describe the motion of bodies in free fall:

where h is the object’s fall height, t denotes the period of fall, u denotes the initial velocity, and v denotes the final velocity when the body accelerates at g.

when addressing numerical issues, the following principles should be kept in mind:

- If an object falls vertically downhill, gravity’s acceleration is considered positive, since the object’s velocity increases throughout the fall.
- If an object is thrown vertically upwards, gravity’s acceleration is considered negative, since the object’s velocity reduces as it ascends.

## Mass

Mass is the overall weight of the body, and it is used to calculate a body’s inertia. It is a scalar quantity with kilogramme as its SI unit.

In other terms, mass refers to the amount of substance contained inside an object.

Regardless of the body’s location in the universe, mass is constant everywhere. The body’s mass cannot be zero.

## Weight

The weight of an object is defined as the force that attracts it to the earth.

**W (Weight) = M (Mass) G (Acceleration Due To Gravity)**

**OR, ****w=****GMm****R****2**** **

**M = Mass Of The Earth And R = Radius Of The Earth**

The following are important factors regarding weight:

- Weight is a vector quantity that works vertically downward and its SI unit is newton (N).
- The mass of one kilogramme is 9.8 N. (i.e. 1 kg-weight equals 9.8 N)
- The weight of an object is not constant, it varies according to its location.
- The weight of an object is zero in the space where g = 0.
- At the earth’s centre, weight is zero. This is because the value of g decreases as one descends to the earth’s core, and g equals zero at the earth’s centre.

**Weight Of An Object On The Moon**

Assume that an item has a mass of m and weight on the moon of wm

Assume the moon has a mass of Mm, and radius of rm

According to the universal law of gravity, an object on the moon

will have a mass of, wm=GMm mRm2 ……….(i)

Consider the moon have a mass of weight of the same object on the surface of the earth to be we. Let Me represents the mass of the earth and Re represent the radius of the earth.

Thus, an object’s weight on the moon is one-sixth that of an object on the earth.

## Thrust and Pressure

Thrust is the force applied perpendicular to the surface of an object. Thrust has a range of effects depending on the region in which it affects.

The unit of thrust is identical to that of force, i.e, Newton as in the SI system (N). It is a vector quantity.

Pressure is the perpendicular force applied on a unit area of an object.

Pressure (p)=Force (F)Area (A)=ThrustArea

The SI unit of pressure is Nm-2 , known as pascal (Pa) after the scientist Blaise Pascal. It is a scalar quantity

**1 Pa = 1 ****Nm****-2**

It is clear from the pressure formula that the same force might exert a varied pressure depending on the region across which it works.

A force operating on a smaller area produces a greater amount of pressure than a force acting on a bigger region.

## Pressure in Fluids

All liquids and gases are collectively referred to as fluids. Water and air are the two most often observed fluids. Due to their mass, solids exert pressure on a surface.

Due to the fact that fluids have weight, they also exert pressure on the base and walls of the container in which they are contained. Pressure is exerted by fluids in all directions.

**BUOYANCY**

- It is called buoyancy when a liquid has a tendency to exert an upward force on an object that is submerged in it. Gases, like liquids, have this characteristic of buoyancy.
- When an object is submerged in a liquid, buoyant force acts upward on it. Additionally, it is referred to as upthrust.
- It is the buoyant force that causes a heavy object to seem lighter when submerged in water. When we lower an object into a liquid, the liquid underneath it exerts an upward force on the object.
- A piece of cork is held under the water’s surface. When we apply pressure to the cork with our thumb, it rapidly rises to the surface.
- The upward thrust exerted by a liquid or a gas at rest on a body partly or totally immersed in it is called buoyant force.

This is because all liquids exert an upward push on the objects submerged in them.

**Experiment: **Take a football. put it into a tub filled with water. it floats with a Large portion of it above the surface of water and only a small portion of it below the surface of water.

Now if we push it into the water , we feel an upward force which opposes the push and we find it difficult to push the ball further into water.

It is also noticed that as the ball is pushed more and more into water, more and more force is needed to push it further into water, till it is completely immersed.

When the ball is inside the water, still a force is needed to keep it inside the water. Now if the ball is released then it bounces back to the surface of water.

**Factors Affecting Buoyant Force**

The magnitude of buoyant force is determined by many factors:

**The Density Of The Fluid :**A liquid with a greater density will exert a greater upward buoyant force on an object than a liquid with a lower density.

This is why swimming in sea water is easier than in freshwater. Because seawater is denser than freshwater, it exerts a stronger buoyant force on the swimmer.

**The Volume Of Object Immersed In The Liquid :**The upward buoyant force grows according to the volume of the solid item submerged in the liquid. The quantity of buoyant force applied on a solid object is independent of its nature. it is entirely dependent on its volume.

When two balls made of different metals with different weights but identical volumes are completely submerged in a liquid, they experience an equal upward buoyant force owing to the fact that both balls displace an equal quantity of liquid due to their equal volumes.

**Floating Or Sinking Of Objects In Liquid**

when an object is submerged in a liquid, it is subjected to the following two forces:

**Buoyant Force**(upthrust) is a force that operates upward, i.e. it tends to push the object higher.- The
**Weight**of an object operates downward, i.e. it tends to pull the object down.

Whether an object floats or sinks in a liquid is determined by the relative magnitudes of these two opposing forces acting on the object.

There are three distinct situations under which objects float or sink. These include the following:

- If the liquid’s buoyant force or upthrust is greater than the thing’s weight, the object will sink in the liquid.
- When the buoyant force equals the object’s weight, then the object will float in the liquid.
- If the buoyant force is greater than the object’s weight, the object will rise to the surface of the liquid and then float.

## Density

A substance’s density is defined as its mass per unit volume

**Density=****Mass of the substance****Volume of the substance**** or ρ=****m****V**

- Density is measured in SI unit as kilograms per metre cube (kg/m3). It is a scalar quantity.

The density of a substance stays constant under specified conditions. Thus, a substance’s density is one of its distinguishing properties. - It may assist us in determining the purity of the substance. It varies according to the substance.

The term density is used to describe the lightness and heaviness of certain substances. - Objects with a density less than the density of a liquid float atop it. Objects with a density higher than that of the liquid sink in it.

It lowers as the temperature rises.

**Effect Of Temperature On Density**

Most of the substances expand on heating and contract on cooling, but their mass remains unchanged.

Therefore, the density of most of the substance decreases with the increase in temperature and vice versa.

**Anomalous Expansion Of Water**

Water shows different expansion from the rest of the liquids. water when cooled from a high temperature it contracts up to 4oc thereafter it expands upto 0oc .

Thus the density of water increases when cooled upto 4oc and then starts decreasing when it is cooled further below 4oc upto 0oc.

## Archimedes’ Principle

When an object is submerged completely or partly in a liquid, it feels a buoyant force or upthrust equal to the weight of liquid displaced by the object.

Even gases, such as air, exert an upward or buoyant force on anything contained inside them. A balloon rises in the air owing to buoyant force or upthrust caused by displaced air.

**Applications Of Archimedes’ Principle**

Archimedes’ principle is used in:

- Specialising in the design of ships and submarines.
- Lacto metre (a device used to determine the purity of milk).
- Hydrometer (a device used to determine a liquid’s density).

## Relative Density

A substance’s relative density is the ratio of its density to that of water.

Relative density of a substance =Density of the substanceDensity of water

In other words, we can say that,

Relative density of a substance =

Mass of the substanceVolume of the substanceVolume of waterMass of water [∵ Densit=MassVolume]

Due to the fact that relative density is a ratio of related quantities, it lacks a unit.

The relative density of a material indicates its weight (or density) in contrast to water. By saying that iron has a relative density of 8.7, we indicate that iron is about 8.7 times the weight of the same amount of water.

**Archimedes’ Principle** is used to precisely determine a substance’s relative density.

## How Does a Boat Float in Water?

A boat floats in water owing to an upward force termed buoyant force (or upthrust), which is created by water pressure pushing up the boat’s bottom.

When a boat is progressively lowered into the water, it begins to displace an increasing amount of water.

As a result, the buoyant force acting on it rises as well. When this buoyant force is sufficient to maintain the boat’s weight, the boat stops sinking in the sea.

Archimedes’ principle now states that “buoyant force equals the weight of liquid displaced by the boat.”

Thus, while the boat is floating, the weight of water displaced by the boat’s submerged section equals the boat’s weight.

## NCERT questions & answers from Gravitation

### State the universal law of gravitation. (CBSE Sample Paper, CBSE 2010, 2011, 2012, 2013, 2015)

**Answer: **The force of attraction between two particles or objectsis

- directly proportional to the product of the masses of the objects and
- inversely proportional to the square of the distance between them.

### Write the formula to find the magnitude of the gravitational force between the earth and an object on

the surface of the earth. (CBSE 2011, 2012, 2013)

**Answer:**

**F =** **GMm/****R****2**

where M = mass of the earth, m = mass of the object, R = radius of the earth.

### What do you mean by acceleration due to gravity ? (CBSE 2011, 2012, 2013)

**Answer:**

The acceleration with which an object falls freely towards the earth is known as acceleration due to gravity. It is denoted by ‘g’.

### What is the difference between the mass of an object and its weight ?

(CBSE 2010, 2011, 2012, 2013)

**Answer:**

**Mass :**

**The quantity of matter contained in a body is called the mass of the body.**

**Mass of a body remains constant.**

**Mass of a body is never zero.**

**Mass is a scalar quantity.**

**Mass is measured in kg.**

**Mass is measured by a beam balance.**

**Weight : **

**The force with which the earth attracts a body towards its centre is called the weight of the body.**

**Weight of a body changes from place to place as it depends on the value ‘g’ and ‘g’ is different at different places.**

**Weight of a body at the centre of the earth is zero.**

**Weight is a vector quantity.**

**Weight is measured in kg wt or N.****Weight is measured by a weighing machine or a spring balance.**

### You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg ?

**Answer:**

Weighing machine gives the weight of an object.

Weight = Mass x g

Thus, mass is less than the weight.

### Gravitational force acts on all objects in proportion to their masses. Why, then, a heavy object does not fall faster than a light object ? (CBSE 2015)

**Answer:**

The acceleration with which a body falls towards the earth is constant (= 9.8 m s-2) and independent of the mass of the body. Thus, all bodies fall with the same acceleration irrespective of their masses. That is why, a heavy body does not fall faster than the light body.

### The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth ? Why ?

**Answer:**

Gravitational force with which a body A attracts another body B is equal in magnitude and opposite in direction to the gravitational force with which a body B attracts the body A.

Thus, the magnitude of force with which the earth attracts the moon is equal to the magnitude of the force with which the moon attracts the earth. Thus, both the earth and the moon attract each other with equal forces.

### If the moon attracts the earth, why does the earth not move towards the moon ?

(CBSE 2011, 2013, 2015)

**Answer:** The acceleration produced in the earth due to the force exerted on it by the moon is very small as the mass of the earth is very large. Hence, the movement of the earth towards the moon is not noticed.

### What is the importance of universal law of gravitation ?

**Answer:**

**The gravitational force plays an important role in nature**

- All the planets revolve around the sun due to the gravitational force between the sun and the planets. The force required by a planet to move around the sun in elliptical path (known as centripetal force) is provided by the gravitational force of attraction between the planet and the sun. Thus, gravitational force is responsible for the existence of the solar system.
- Tides in oceans are formed due to the gravitational force between the moon and the water in oceans.
- Gravitational force between a planet and its satellite (i.e., moon) decides whether a planet has a moon or not. Since the gravitational force of the planets like mercury and venus is very small, therefore, these planets do not have any satellite or moon.
- Artificial and natural satellites revolve around the earth due to the gravitational force between the earth and the satellite. The gravitational force between the earth and the satellite provides a necessary centripetal force to the satellite to move in a circular path around the earth.
- The atmosphere (envelope of gases) of the earth is possible due to gravitational force of the earth.
- Rainfall and snowfall is possible only due to gravitational force of the earth.
- We stay on the earth due to the gravitational force between the earth and us.