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,$\textbf{F}&space;=&space;\frac{\textbf{GMm}}{\textbf{d}^{\textbf{2}}}$
Where, G is constant of proportionality and is known as universal gravitation constant.

Universal Gravitation Constant (G):-

• $\textbf{G&space;=&space;}&space;\frac{\textbf{Fd}^{\textbf{2}}}{\textbf{Mm}}$
• 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
$\textbf{g&space;=&space;}&space;\frac{\textbf{GM}}{\textbf{R}^{\textbf{2}}}$

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 = Mm = 7.36 x 1022 kg
mass of earth = Me = 5.98 x 1024 kg
Radius of moon = Rm = 1.74 x 106 m
Radius of earth = Re = 6.36 x 106 m
Weight of object on moon = $W_{m}&space;=&space;\frac{GM_{m}m}{R_{m}^{2}}$
Weight of object on earth = $W_{e}&space;=&space;\frac{GM_{e}m}{R_{e}^{2}}$

Now,
Wm/We = (GMmm/Rm2)/(GMem/Re2)

On putting the given values and solving, we get:
Wm/We = 0.165 ≈ ⅙
Or, Wm = ⅙We

Or, mgm = ⅙ mge
So, gm = ⅙ ge

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