Question

state and drive the universal law of gravitation

Answer 1

State the universal law of gravitation.  Universal law of gravitation:  The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.   Derivation:  For two objects of masses m1 and m2 and the distance between them r, the force (F) of attraction acting between them is given by the universal law of gravitation as:


you can see upward

Answer 2

Answer:

Explanation:

Universal Law of Gravitation

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 square of the distance between them. The force is along the line joining the centres of two objects.

 

 

Fig.1

 

Let two objects A and B of masses M and m lie at a distance d from each other as shown in Fig. 1.. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,

                                    F  M*m           ---------- (1)                                                    

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

                                    F α 1 ⁄ d2       ---------- (2)

                                                           

Combining Eqs. (1) and (2), we get

                     

                               F α M x m ⁄ d2      ---------- (3)

                   or, F = G( (M x m) ⁄ d2)    ---------- (4)                                    

 

                         

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

                             F × d 2 = G M × m

   or                       G  = F d2/ M m        ---------- (5)            

                                                     

The SI unit of G can be obtained by substituting the units of force, distance and mass in Eq. (5) as N m2 kg–2.

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

G is 6.673 × 10–11 N m2 kg–2.