Physics

# Gravitation

Gravitational force is always attractive, conservative and independent of medium and acts on line foining the centres of the bodies.

Newton's law of gravitation:

Force acting between two bodies directly proportional to product of the masses and inversly proportional to square of distance between them.

Given by,

where G= Universal gas constant=

Gravity is the phenomenon of attraction of surrounding bodies to centre of particular body and is a vector quantity It holds the atmosphere around earth.

Given by:

so,

so,

Variation of acceleration due to gravity

1.with height

= for h< < R

2.With depth

At center of earth g'=0; x=R

3.With rotation of earth

At equator, ;

At poles, ; There is no effect of rotation at poles

Gravitational intensity: It is the force experienced by unit point mass placed at that point of consideration with gravitational field . It is scalar quantity.

Gravitational Potential (V): It is work done to take a unit mass from infinity to a certain point of consideration within gravitational field.field . It is scalar quantity.

Gravitational potential energy: It is work done to take a body of mass m from infinity to a point of consideration within gravitational field.

Gravitational potential energy on height h from the surface of earth

Its maximum value is 0 to infinity.

Change in gravitational PE when a body is raised from surface to height h is

=

Gravitational potential and intensity are related as

Gravitational field and potential

1.For point mass at distance r,

and

2.For hollow sphere of mass M having radius R

i. Outside point (r>R): and

ii. On the surface (r=R): and

iii. Inside point (r and

3.For solid sphere of mass M and radius R

i. Outside point (r>R): and

ii. On the surface (r=R): and

iii. Inside point (r and

4.For ring of radius R, mass M on its axis

#If two point masses and are kept at distance r then field intensity becomes zero at a distance

Motion of satellites

Time period

For nearer satellite, r=R so,

and = 84.6 min

Geostationary satellite appears stationary with respect to earth and launched on equateral plane (time period t = 24 hours) and height= 36,000 km

Energy of satellite

P.E. =

K.E.== binding energy

T.E. = P.E. + K.E.= = (PE=2TE=-2KE)

If a body is projected from earth then the maximum height attained by it is

or,

or,

so,

For escape velocity, h called escape velocity = 11.2 km/s for each

So, on increasing the orbital velocity of satellite by 41.4% the satellite escapes ( or KE by 100%)