Gravitation Class 9th Notes - Free NCERT Class 9 Science Chapter 10 Notes - Download PDF

NCERT Notes for Class 9 Science Gravitation: Download PDF

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NCERT Notes for Class 9 Physics Chapter 9

Gravitation

Gravitation is the force of attraction between any two objects in the universe. It was first explained by Sir Isaac Newton

Newton's Observations

• Apple falls on the ground because the earth attracts it towards itself.

• Can Apple also attract the earth? - Yes. apple also attracts the earth as per Newton's third law. But the mass of the earth is extremely larger than Apple's mass hence, the force applied by Apple is negligible and Earth never moves towards it.

• Newton then suggested that every object in this universe attracts another object. This force of attraction is called Gravitational Force.

Universal Law of Gravitation

Newton proposed a law that we call Newton's law of Gravitation. According to this law. "Every particle in the universe attracts every other particle with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between the two masses. The direction of force is along the line joining the two particles."

Consider two particles $A$ and $B$ of masses $m_1$ and $m_2$ respectively separated by a distance $r$ as shown in figure.

If $F$ is the force of attraction between $A$ and $B$, then

$
\begin{aligned}
& F \propto m_1 \times m_2 -----(i)\\
& F \propto \frac{1}{r^2}-----(ii)
\end{aligned}
$
Combining (i) and (ii), we get

$
\begin{aligned}
& F \propto \frac{m_1 m_2}{r^2} \\
& F=\frac{G m_1 m_2}{r^2}
\end{aligned}
$

where $G$ is the constant of proportionality called the universal gravitational constant.

$
G=\frac{F r^2}{m_1 m_2}
$

The SI unit of universal gravitational constant is $\frac{\mathrm{Nm}^2}{\mathrm{~kg}^2}$ and its numerical value is found to be,

$
G=6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2
$

This force between any two particles is not altered by the other objects, even if they are located between the particles.

Properties of Gravitational Force

1. It is independent of the medium between the particles.
2. It is always attractive in nature.
3. It is the weakest force in nature.
4. It is a conservative force i.e., the work done by it on a particle doesn't depend on the path taken by the particle; or the work done in moving a particle round a closed path under the action of gravitational force is zero.
5. The magnitude of force with which one body (say the earth) attracts the second body (say an apple) is equal to the magnitude of force with which second body (say apple) attracts the first body (in accordance with Newtons $3^{\text {rd }}$ law).
6. It is a two body interaction i.e., gravitational force between two particles is independent of the presence or absence of other particles.
7. It is a central force i.e., acts along the line joining the two particles or centres of the interacting bodies.

Applications of Newton's Law of Gravitation

Following are the applications of Newton's law of gravitation :
1. It helps us to determine the mass of the earth, the sun, the moon and the planets.
2. To determine the motion of the moon around the earth.
3. To describe the motion of planets around the sun.
4. To describe the tides due to the moon and the sun.
5. To estimate the mass of the double stars.
6. It helps us to discover new stars and planets.

Importance of the Universal Law of Gravitation

The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:

(i) the force that binds us to the earth;
(ii) the motion of the moon around the earth;
(iii) the motion of planets around the Sun; and
(iv) the tides due to the moon and the Sun.

Free Fall

When an object falls towards the earth because of the earth’s gravity and there is no other force acting upon it, the object is in a free-fall state. Air resistance is negligible.

The value of ‘g' is the same on the earth, thus the equations of motion for an object with uniform motion are valid.

$\begin{aligned} & v=u+g t \\ & s=u t+g t^2 / 2 \\ & 2 g s=v^2-u^2\end{aligned}$

To Calculate the Value of g

To calculate the value of $g$, we should put the values of G, $M$ and $R$ in Eq. (9.9), namely, universal gravitational constant, $\mathrm{G}=6.7 \times 10^{-11}$ $\mathrm{N} \mathrm{m}^2 \mathrm{~kg}^{-2}$, mass of the earth, $M=6 \times 10^{24} \mathrm{~kg}$, and radius of the earth, $R=6.4 \times 10^6 \mathrm{~m}$.

$
\begin{aligned}
g & =\mathrm{G} \frac{M}{R^2} \\
& =\frac{6.7 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2} \times 6 \times 10^{24} \mathrm{~kg}}{\left(6.4 \times 10^6 \mathrm{~m}\right)^2} \\
& =9.8 \mathrm{~m} \mathrm{~s}^{-2}
\end{aligned}
$

Thus, the value of acceleration due to gravity of the earth, $g=9.8 \mathrm{~m} \mathrm{~s}^{-2}$.

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

In the case of free fall, acceleration of the body is uniform, which is independent of the mass of the body. Therefore, all the equations of uniformly accelerated motion of the bodies become valid with acceleration ' $a$ ' replaced by ' $g$ '.
$v=u+g t \quad(a$ replaced by $g$ in $v=u+a t)$
$h=u t+\frac{1}{2} g t^2 \quad\left(s\right.$ replaced by $h$ and $a$ replaced by $g$ in $\left.s=u t+\frac{1}{2} a t^2\right)$
$v^2=u^2+2 g h \quad\left(s\right.$ replaced by $h$ and a replaced by $g$ in $\left.v^2=u^2+2 a s\right)$

Mass

Mass : Mass of a body is the quantity of matter contained in it. It remains same whether the object is on the earth, the moon or anywhere in space. Thus, the mass of a body remains constant. The mass of a body is the measure of its inertia and hence, it is also known as inertial mass. It is a scalar quantity and cannot be negative. The SI unit of mass is kilogram and represented by (kg).

Weight

The weight of a body on earth is the force with which it is attracted towards the centre of the earth.
According to Newton's second law,

$
F=m a=\text { mass } \times \text { acceleration }
$

The acceleration produced by the gravitational force is known as the acceleration due to gravity (g).

$
\therefore \quad F=m g
$

By definition of weight, the force of attraction of the earth on a body, is the weight of the body on earth. It is denoted by $W$.

So, $W=m g$
* The SI unit of weight is same as the force i.e., newton.

$
1 \mathrm{~N}=1 \mathrm{~kg} \mathrm{~m} / \mathrm{s}^2
$

* The weight is a force which acts vertically downward.
* It is a vector quantity. It has both magnitude and direction.

Weight of an Object on the Moon

The weight of an object depends on the gravitational force acting on it. Since the Moon's gravity is about one-sixth of Earth's gravity, an object will weigh six times less on the Moon than it does on Earth.

The formula for weight is:

$
\text { Weight }(\mathrm{W})=\text { mass }(\mathrm{m}) \times \text { acceleration due to gravity }(\mathrm{g})
$

On the Moon:

$
W_{\text {moon }}=m \times g_{\text {moon }}=m \times \frac{1}{6} g_{\text {earth }}
$

So, if an object weighs 60 N on Earth, it would weigh about 10 N on the Moon. However, its mass remains the same both on Earth and the Moon.

Thrust and Pressure

The net force acting on an object perpendicular to its surface is called thrust. The normal force per unit area is called pressure.

Pressure : The thrust on unit area is called pressure.
Thus, Pressure $=\frac{\text { Thrust }}{\text { Area }}$
Pressure is a scalar quantity.
SI unit of Pressure : By putting the SI unit of thrust ( N ) and area ( $\mathrm{m}^2$ ) in the above relation, we get $\frac{\text { newton }}{\text { metre }^2}$ or $\frac{\mathrm{N}}{\mathrm{m}^2}$

Pressure in Fluids

Fluids (liquids and gases) exert pressure in all directions. The pressure at a point in a fluid increases with depth and depends on the density of the fluid and gravitational force.

The formula for pressure in a fluid is:

$
\begin{gathered}
\text { Pressure }(\mathrm{P})=\operatorname{density}(\rho) \times \operatorname{gravitational~acceleration}(g) \times \text { height }(\mathrm{h}) \\
\qquad P=\rho g h
\end{gathered}
$

Buoyancy

Every fluid exerts an upward force on a body immersed in it. This upward force is called buoyant force or buoyancy.

Buoyant force depends on:

• The volume of fluid displaced
• The density of the fluid

Formula (for buoyant force):

$
\text { Buoyant Force }=\rho \times g \times V
$

Why Objects Float or Sink When Placed on the Surface of Water

A thing made of wood floats over the surface of water, but a small pin made of iron when put on the surface of water, sinks to the bottom.

It can be understood by considering the number of forces acting on a body when it is immersed in a liquid.
When a body is immersed in a liquid, there are two forces acting on the body as given below
(i) Weight of the body acts vertically downward, which has tendency to sink the body in the liquid due to gravity.
(ii) Upward thrust of the liquid acts vertically upward, which is equal to the weight of the liquid displaced by the immersed part of the body. This force has a tendency to push the body out of the given liquid.

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