Class 9 Gravitation Notes

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/d²
On combining:
F ∝ Mm/d²
or, $\textbf{F} = \frac{\textbf{GMm}}{\textbf{d}^{\textbf{2}}}$
Where, G is constant of proportionality and is known as universal gravitation constant.

Universal Gravitation Constant (G):-

$\textbf{G = } \frac{\textbf{Fd}^{\textbf{2}}}{\textbf{Mm}}$
S.I. unit of G:- N m² kg^-2
G = 6.673 x 10^-11 N m² 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/d²
or, F = G Mm/R² ————-(ii)
Where, ‘M’ is mass of earth & ‘R’ is radius of earth.
From (i) & (ii)
mg = G Mm/R²
$\textbf{g = } \frac{\textbf{GM}}{\textbf{R}^{\textbf{2}}}$

Calculation of value of ‘g’ :-

Mass of earth = M = 6 x 10²⁴ kg
Radius of earth = R = 6.4 x 10⁶ m
& g = 6.7 x 10^-11 N m² kg^-2
g = GM/R²
Or, g = (6.7 x 10^-11 x 6 x 10²⁴)/(6.4 x 10⁶)²
Or, g = 40200/4096
Or, g = 9.8 m/s²

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 10²² kg
mass of earth = M_e = 5.98 x 10²⁴ kg
Radius of moon = R_m= 1.74 x 10⁶ m
Radius of earth = R_e = 6.36 x 10⁶ m
Weight of object on moon = $W_{m} = \frac{GM_{m}m}{R_{m}^{2}}$
Weight of object on earth = $W_{e} = \frac{GM_{e}m}{R_{e}^{2}}$

Now,
W_m/W_e = (GM_mm/R_m²)/(GM_em/R_e²)

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/m² or, 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 m² 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/m³
Density of water = 1000 kg/m³ = 1 g/cm³

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

Class 9