# Class 9 Gravitation Notes

Notes Important Questions**Gravitation Notes**

## Gravitational force:-

The force of attraction between any two objects in the universe is called gravitational force.

## Universal law of gravitation:-

Every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

## Mathematical formulation of universal law of gravitation:-

Consider two objects of masses ‘M’ & ‘m’ separated by a distance ‘d’.

F ∝ Mm

& F ∝ 1/d^{2}

On combining:

F ∝ Mm/d^{2}

or,

Where, **G** is constant of proportionality and is known as universal gravitation constant.

## Universal Gravitation Constant (G):-

- S.I. unit of G:- N m
^{2}kg^{-2} - G = 6.673 x 10
^{-11}N m^{2}kg^{-2}

## Importance Of The Universal Law Of Gravitation:-

The universal law of gravitation successfully explained some phenomena like:

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

## Free fall:-

When an object falls towards the earth due to gravitational force only then the object is said to be in free fall.

## Acceleration due to gravity (g):-

Consider an object of mass ‘m’ near the surface of the earth.

Using 2nd law of motion,

F = ma

F = mg (Where, g is acceleration due to gravity) ———-(i)

Using universal law of gravitation,

Since, F = G Mm/d^{2}

or, F = G Mm/R^{2} ————-(ii)

Where, ‘M’ is mass of earth & ‘R’ is radius of earth.

From (i) & (ii)

mg = G Mm/R^{2}

## Calculation of value of ‘g’ :-

Mass of earth = M = 6 x 10^{24} kg

Radius of earth = R = 6.4 x 10^{6} m

& g = 6.7 x 10^{-11} N m^{2} kg^{-2}

g = GM/R^{2}

Or, g = (6.7 x 10^{-11} x 6 x 10^{24})**/**(6.4 x 10^{6})^{2}

Or, g = 40200**/**4096

Or, g = 9.8 m**/**s^{2}

- The value of g is not constant at all points on the surface of the earth as it is not a perfect sphere.
- At the poles, the value of g is greater than at the equator as the radius of the earth increases from poles to equator.
- The value of g is zero (0) at the centre of the earth.
- The value of g increases from centre to surface and then decreases while going up from the surface.
- Acceleration due to gravity is independent of mass. So, all objects fall at the same rate under the gravitational force only.

## Mass:-

The quantity of matter present in a body is called its **mass**.

- S. I. unit of mass:-
**Kg** - It is a
**scalar**quantity. - Mass of an object is constant at all points in the universe.

## Weight:-

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

- From 2nd law of motion,

F = ma

Or,**W = mg** - S. I. unit:-
**Newton (N)** - It is a
**vector**quantity. - It is not constant at all points in the universe.

## Weight of an object on moon:-

Consider an object of mass ‘m’ .

mass of moon = M_{m} = 7.36 x 10^{22} kg

mass of earth = M_{e} = 5.98 x 10^{24} kg

Radius of moon = R_{m }= 1.74 x 10^{6} m

Radius of earth = R_{e} = 6.36 x 10^{6} m

Weight of object on moon =

Weight of object on earth =

Now,

W_{m}/W_{e} = (GM_{m}m**/**R_{m}^{2})/(GM_{e}m**/**R_{e}^{2})

On putting the given values and solving, we get:

W_{m}**/**W_{e} = 0.165 ≈ ⅙

Or, **W _{m} = ⅙W_{e}**

Or, mg_{m} = ⅙ mg_{e}

So, **g _{m} = ⅙ g_{e}**

## Thrust:-

The perpendicular force acting on the surface of an object is known as **thrust.**

- S.I. unit of thrust:- Newton (N)

## Pressure:-

The thrust acting on unit area is called **pressure**.

**Pressure = Thrust/Area**- S.I. unit of pressure:-
**N/m**or,^{2}**Pascal (Pa)** - On increasing the force, pressure on an object also increases and vice-versa.
- On increasing the surface area, pressure on an object decreases.

**1 Pascal:-** The pressure acting on an object is said to be 1 pascal when 1 N perpendicular force is acting on 1 m^{2} area.

#### Pressure in fluids:-

The pressure exerted by a fluid in a container is transmitted undiminished in all directions.

## Buoyant Force/Upthrust:-

The upward force exerted by a fluid on a substance when immersed in it is called **upthrust**.

- The magnitude of the buoyant force depends on the density of the fluid.

## Density:-

The mass per unit volume of an object is known as its **density**.

**Density = mass/volume**- S.I. unit:-
**kg/m**^{3} - Density of water = 1000 kg/m
^{3}= 1 g/cm^{3}

- If the density of object is more than the density of fluid, it will sink.
- If the density of object is less than the density of fluid, it will float.

## Archimedes’ Principle:-

When a body 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.*i.e., Buoyant force = Weight of the fluid displaced*

#### Applications of Archimedes’ Principle:-

- Ships and submarines are designed on this principle.
- It is used to design lactometers.
- It is used to design hydrometers.

**Lactometer:- **It is used to determine purity of milk.

**Hydrometer:-** It is used to determine density of liquid.

## Relative Density:-

The ratio of density of substance to the density of water is known as the **relative density** of substance.

**Relative density = Density of substance/ Density of water**- Relative density has no unit.

For the important questions of gravitation, click https://brainigniter.in/class-9/physics-gravitation-important-questions

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