Question

1. Explain, universal low of grovitation.

​

Answer 1

Law of gravitation-
According to this law, any two body at some distance having mass will feel an attraction force, this law is universal because it is applicable to any body in universe having mass.

If two bodies having mass m
1
​
and m
2
​
are at a distance r any time then the force of gravitation F is given as F=
r
2

Gm
1
​
m
2
​

​

its vector form is like this
F
=
r
3

−Gm
1
​
m
2
​

​

r

The minus sign denote that its force of attraction that is opposite to distance vector
r
from one mass to second mass .
G is universal gravitational constant having value 6.7×10
−11
in M.K.S. unit.


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Answer 2

[ Refer to an attachment ]

${ \underline{ \sf{Correct \: Question :}}}$

• Explain Universal Law Of Gravitation.

${ \underline{ \sf{Required \: Answer :}}}$

Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the the square of the the distance between them. The force is along the line joining the centres of two objects.

Let two objects A and of masses M and m lie at a distance d from each other as shown in picture. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two object is directly proportional to the product of their masses. That is

${ \green{ \boxed{ \sf{F \: ∝ \: M \times m}}}} - - - - \: { \sf{(1)eq.}}$

And the force between two objects is inversely proportional to the square of the distance between them, that is

${ \blue{ \boxed{ \sf{F∝ \frac{1}{d^{2} }}}}} - - - - \: { \sf{ (2) eq.}}$

Combining Equation 1 and 2, we get

${ \red{ \boxed{ \sf{F∝ \frac{M \times m}{d^{2} } }}}} - - - - { \sf{(3)eq.}}$

• Or,

${ \pink{ \boxed{ \sf{F = G \frac{M \times m}{d^{2} } }}}} - - - - { \sf{(4)eq.}}$

Where G is the constant of proportionally and is called the universal gravitation constant. By multiplying crosswise, Eq. (4). gives

${ \orange{ \boxed{ \sf{F \times d^{2} = G \: M \times m}}}}$

• Or,

${ \purple{ \boxed{ \sf{G = \frac{Fd ^{2} }{M \times m} }}}} - - - -{ \sf {(5)eq.}}$

The SI unit of G can be obtained by substituting the units of force, distance and mass in Eq. (5) as :-

${ \boxed{ \sf{N \: m^{2} Kg^{ - 2} }}}$

The value of G it was found out by Henry Cavendish ( 1731 - 1810 ) by using a sensitive balance. The accepted value of G is :

${ \boxed{ \sf{6.673 \times 10 ^{ - 11} N \: m^{2} Kg ^{ - 2} }}}$

• Importance of the UNIVERSAL LAW OF GRAVITATION :-

The universal law of gravitation successfully explain several phenomena which were believed to be unconnected :

• the force that binds us to the earth ;

• the motion of the moon around the earth ;

• the motion of planets around the sun ;

• the tights due to the moon and the sun.

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