GRAVITATION NOTES(Sara’s)

Newton’s law of gravitation:-

Newton's Law of Universal Gravitation states that every particle attracts every other
particle in the universe with force directly proportional to the product of the masses and
inversely proportional to the square of the distance between them.
● F ∝ m1m2
● F ∝ 1/r2
● F ∝ m1m2/r2
● F = G m1m2/r2 (G= universal constant of gravitation)

Universal Constant of Gravitation:-

Gravitational force acting between two bodies of one unit mass, kept at a unit distance
from each other.
F = G m1m2/r2
F = G x 1 x 1/12 (All values at one unit)
Hence ,F = G
Gravitation is a weak force unless large masses are involved.
It was founded by Henry Cavendish by using a sensitive balance.
The value of G is a universal constant and doesn't change.
G = 6.67×10-11Nm2/kg2.
SI = 6.67×10-11 Nm2/kg2. CGS = 6.67×10-8 dyne cm2/g2

Importance of Universal law of Gravitation:-

1. Force that binds us to earth.
2. Motion of moon around the earth.
3. Revolution of planets around the Sun.
4. Tides of Sea due to the moon and Sun..

Centripetal Force:-
Centripetal force is the force on an object on a circular path that keeps the object moving
on the path. It is always directed towards the centre.

Acceleration due to gravity:-

Acceleration due to gravity is the acceleration an object gains due to the force of gravity.
It is a vector quantity.The symbol (g) is used to represent it.
The acceleration due to gravity is independent of the mass of the object.
According to the law of gravitation:-
F = GMm/r2
According to the second law of motion:-
F=mg
GMm/r2 = mg
g = GM/r2
Value of (g) on the surface of Earth:-

Free Fall:-
Free fall is the motion of an object under the influence of gravity alone. It's a natural
phenomenon that occurs on Earth when an object falls towards the ground.

Difference between ‘g’ and ‘G’:-

Acceleration due to gravity (g) Universal gravitational constant (G)

1.The acceleration produced in a body 1. The gravitational force between two

falling freely under the action of bodies of unit masses separated by a unit
gravitational pull of the earth is known as distance is known as universal
acceleration due to gravity. gravitational constant.

2. The value of ‘g’ is different at different 2. The value of ‘G’ is the same at every
points on the earth.Therefore, it’s a point on the earth.Therefore, it’s a
variable. universal constant.

3. The value of ‘g’ at the centre of the 3. The value of ‘G’ is not zero at the centre
earth is zero. of the earth or anywhere else.

4. The value of ‘g’ is different on the 4. The value of ‘G’ is the same throughout
surface of different heavenly bodies like the universe.
the sun, moon, and the planets.

5. The value of ‘g’ on the surface of the 5. The value of G = 6.673 × 10-11 Nm2 kg-2
earth is 9.8 ms-2. throughout the universe.
Difference between mass and weight:-

Mass Weight

1. Mass is the quantity of matter possessed 1. Weight is the force with which a body is
by a body. attracted towards the centre of the earth or
any celestial body.

2. It is a scalar quantity. 2. It is a vector quantity.

3. It's S.I. unit is kilogram (kg.) 3. It's S.I. unit is Newton (N).

4. Mass of a body remains constant at all 4. Weight of the body changes from place
places to place.

5. Mass of a body is never zero. 5. Weight can be zero when acceleration

due to gravity is zero.

6. Mass is measured by a beam 6. Weight is measured by a spring balance.

balance/weighing scale/physical balance.

Variation of (g):-
The value of gravitational acceleration, or (g), varies due to a number of factors:
Latitude
The value of (g) is highest at the poles and lowest at the equator. This is because the Earth
is not a perfect sphere, but is flattened at the poles and bulges at the equator. The radius
of the Earth is greater at the equator, so the acceleration due to gravity is smaller there
and higher at the pole.
Altitude
The value of (g) decreases as you move away from the Earth's surface. This is because the
radius of the Earth increases as you go higher and (g) is inversely proportional to the
square of the radius.
Depth
The value of (g) decreases as you move deeper into the Earth as the radius or the distance
from the centre decreases and becomes zero at the centre.

Free Fall is governed by three equations of motion:-

v=u+at → v=u+gt
s=ut+½ at2 → h=ut+1/2gt2
v2=u2+2as → v2 = u2 + 2gh
Thrust:-
Thrust is a force that acts on an object perpendicular to its surface.It depends upon the
area on which it acts.
It is a vector quantity
The SI unit of thrust is Newton (N).
Thrust = Pressure*Area
Pressure:-
The thrust on a unit surface area is called Pressure.
It is a scalar quantity.
The SI unit of pressure is N/m2 (Pascal(Pa))
Pressure = Thrust/Area (Area and Pressure are inversely proportional.)
Fluid:-
Substances which can flow easily because of increased intermolecular spaces and do not
have fixed shape are called fluids.
Characteristics:
Fluids exert force on the walls and the base of the container.
Pressure exerted by fluid is transmitted undiminished in all directions without reduction.
Pascal's law says that pressure applied to an enclosed fluid will be transmitted without a
change in magnitude to every point of the fluid and the walls of the container.

Liquid Pressure:-
Liquid pressure is the increase in pressure at increasing depths in a liquid.
Pressure exerted by the liquid is due to the weight of the liquid.
Characteristics
At a given depth pressure remains the same.
It depends on the height and depth of the liquid.
As you go deeper, the pressure increases because the object below has to support the
weight of the liquid above it.
Directly proportional to
The gravitational field strength
The depth
The density of the liquid
Pressure caused by liquid:- P = hpg(height*density*gravity)
Pressure in a liquid:- P = hpg + Patm (atmospheric pressure.)

Difference between Solid pressure and Fluid Pressure:-

Solids exert pressure in a downward direction, while fluids exert pressure in all
directions. This is because the molecules of fluids collide and move rapidly thus crashing
with the walls and surface of the container.

Buoyant Force(Upthrust):-
Buoyant force is a force that is exerted on an object which is partially or completely
immersed in a fluid.This phenomenon is called Buoyancy.
FB = W – Object will be Partially Submerged
FB < W – Object will Float
FB > W – Object will Sink
FB = gpV
g is the acceleration due to gravity of 9.8m/s2
p is the density of water
V is the volume of displaced fluid
The greater the density of a fluid, the greater the buoyant force it exerts on an object.
The greater the volume of fluid displaced by an object, the greater the buoyant force it
experiences.

Archimedes Principle:-
This Principle states that an object placed in a fluid experiences an upward force, called
buoyant force, that is equal to the weight of the fluid displaced by the object.
Applications
It is used in designing ships and submarines.
It is used in hydraulic lifts.
It is used in hydrometers to determine density of liquids in relation to water.
It is used in lactometers to determine the purity of milk.
Density:-
Mass per unit volume of a substance is called Density.
Its SI unit is kg/m3
Objects having a lesser density than the fluid will float whereas if it has a higher density,
it will sink. An object with the same density as water will be neutrally buoyant in water,
meaning it will neither sink nor float, but remain suspended.

Relative Density:-
Relative density, also called specific gravity, is a dimensionless quantity defined as the
ratio of the density of a substance to the density of water.
It is a unitless quantity.
The density of pure water is 1 gm/cm3 or 1000 kg/m3.
Relative Density = Density of substance/Density of water at 4oc.
Weight = Mass*Gravity
Density = Mass/Volume
Mass = Density*Volume
Hence,Weight = Volume*Density*Gravity