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Class 9, Science, Chapter-9, Lecture-1, Gravity (Notes)

Gravitation: 

The attraction between any two objects of the universe is called Gravitation.

Gravity: 

The force with which a planet attracts an object is called its gravity.

Difference between:

Gravity

Friction

1. It can produce acceleration as well as retardation

1. It always produces retardation.

2. It can produce acceleration as well as retardation

2. It acts only when two objects are in contact.

Newton’s Law of Universal Gravitation: 

“Any two bodies in the universe attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the centres of bodies”.

Mathematically: 

$F \propto {{{m_1} \times {m_2}} \over {{d^2}}}$

$ \Rightarrow $ ${F = G.{{{m_1} \times {m_2}} \over {{d^2}}}}$ (Where G is constant known as Universal Gravitational Constant) 

Unit of ‘G’
$G = {F \over {{{{m_1}{m_2}} \over {{d^2}}}}}$
$ \Rightarrow $ S.I. Unit of G = ${{S.I.{\rm{ ~Unit~ of~ force}}} \over {{{S.I.{\rm{ ~Unit ~of ~}}{{\rm{m}}_1} \times S.I.{\rm{ ~Unit ~of ~}}{{\rm{m}}_2}} \over {S.I.{\rm{ ~Unit ~of~ }}{{\rm{d}}^2}}}}}$ = ${N \over {{{kg \times ~kg} \over {{m^2}}}}}$ = ${{N{m^2}} \over {k{g^2}}}$

${\therefore~}{S.I.{\rm{ ~Unit~ of~ G ~ =  N}}{{\rm{m}}^2}k{g^{ - 2}}}$ AND ${{\rm{cgs~ unit~ of~ G~ }} = dync{m^2}{g^{ - 2}}}$

Value of G

${G = {F \over {{{{m_1} \times {m_2}} \over {{d^2}}}}}}$

If , ${{\rm{m}}_{\rm{1}}}{\rm{ = }}{{\rm{m}}_{\rm{2}}}{\rm{ = 1 and d = 1}}$,

$G = {F \over {{{1 \times 1} \over 1}}} = F$

$ \Rightarrow $ ${G = F}$

Universal Constant of Gravitation is numerically equal to the force of attraction between two bodies of unit mass which are separated by a unit distance.

  • In S.I. Unit $G = 6.673 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}$
  • In cgs Unit $G = 6.673 \times {10^{ - 8}}dync{m^2}{g^{ - 2}}$

Newton’s Third Law and Gravitation: 

Two bodies attract each other with equal and opposite force, but the acceleration produced may be different. 
$F = m.a$
$ \Rightarrow a = {F \over m}$

$ \Rightarrow a \propto {1 \over m}$

for small mass, ‘a’ will be greater 
for large mass, ‘a’ will be smaller