Gravitation

Gravitation

The phenomenon of attraction between different bodies in the universe

Gravity

Force exerted by earth or any other object on other objects.

Centripetal force

The force that causes acceleration and keeps the object moving along the circular path.
Eg: motion of moon around earth.

Newton's universal law of gravitation

Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The force act along the line joining the centre of two bodies.

universal gravitational constant

It is equal to the force of attraction acting between two bodies each of unit mass whose centers are placed at unit distance apart.

Formula for universal gravitational constant

G = (Fd^2)/m1*m2

SI unit of Universal Gravitational Constant

Nm2/kg2

G =

6.673 x 10^-11 Nm2/kg2

Value of G was found out by

Henry Cavendish by using a sensitive balance.

Newton's law of gravitation is also called

Inverse square law as the force of attraction (F) between two bodies as it is inversely proportional to the square of the distance between (d) between them.

Importance of Universal law of Gravitation

It is the force that binds us to the earth.
The motion of planets around the sun.
Atmosphere near the surface of the earth.
Formation of tides due to the moon and the sun.

Free fall

Whenever objects fall towards the earth only under the force of gravity (with no other forces acting on it) we say the objects are in state of free fall.

Acceleration due to gravity

The uniform acceleration produced in a body when it falls freely under the effect of gravity is known as acceleration due to gravity.

Relation between g and G

g = GM/R^2

g depends on

mass and radius

g of earth =

GM/R^2 of earth which is 9.8 m/s^2 where G = 6.673 x 10^-11; M = 6x10^24 kg; R = 6.4x10^6 m

Features of acceleration due to gravity

The value of 'g' increases as we go from equator to the poles (g α 1/R2)
The value of 'g' decreases with height (altitude) (g α 1/R2)
The value of 'g' is maximum at earth's surface and decreases with depth and becomes zero at the center of the earth.

Gravity of moon is

1.63 m/s^2 (1/6th gravity of Earth)

Formulae for freely falling bodies

v=u+at
h=ut+1/2 gt^2
v -u =2gh

When a body is thrown up, g is

-ve. It's positive when the body falls down.

Is time of ascent equal to time of descent?

YES

Mass

It is the amount of matter contained in a body. It is a scalar quantity. It is a constant everywhere.

SI/CGS unit of mass

1. kg 2. gm

Weight

It is the amount of gravitational pull acting on an object. It is a vector quantity. It varies from place to place.

SI/CGS unit

1. Newton 2. Dyne

W =

Mg

Thrust

The force acting on an object perpendicular to the surface

SI unit of thrust is

Newton

Pressure

Thrust per unit area

SI unit of pressure

N/m^2 - Pascal

CGS unit of pressure

Dyne/cm^2

Pressure is directly proportional to

force/thrust

Pressure is indirectly proportional to

area

1 cm^2 is equal to

10^-4 m^2

1 cm^3 is equal to

10^-6 m^3

Fluid

Any substance which has a fixed shape and has the ability to flow is called a fluid.

All points at the same depth in a liquid are under

same pressure