Newton's Gravity Continued...

http://vaibhavkhamgaonkar.blogspot.com/2011/05/newtons-gravity.html
                                            (link to previous post)

As in the previous post we have found out the Newtons most famous equation i.e. Law of Gravitation which is given by

F = G*(m1 * M2)/r^2
where G is the gravitational constant = 6.67 * 10 ^-11
m1 & M2 are the masses of an object experiencing gravitational force.
r is the distance between two object.


Now lets see what does it mean, it simply tells that if a objects having mass (m1 & M2) which are separated by certain distance (r) then according to Newton, they will experience some kind of attraction (they will experience force of attraction) which depends on products of there Masses & the Square of Distance between them. This is often called as Inverse square law.


Now with this we can find the force of attraction between two object. But wait if it is true that two object separated by certain distance they will experience a force then why we not experiencing that force since we are pretty close to various objects around us.
let me clarify you, in day today life we used to pass through various objects but we haven't experience that kind of attraction.
Why ?
Well if you look at the Equation carefully, there is a term called Gravitational constant "G" & whose value is very very small. now if u thing that u should experience the same kind of force then the only thing is to overcome that value is the mass but  you don't have enough mass to overcome thus we aren't experience this force. This phenomenon occurs only for the the objects whose mass is very very high (like Planets, Stars, Galaxies etc)

Now just tell me that if you are having two objects of different masses lets say 1 is of 1Kg & other is of 10 kg. they both are falling from 100 stories building. so which one will fall first on the ground if they are start falling at same time...?

If u say that they will going to fall at same time then u are corrects....
let me tell u how :-

what is the force:-
F = m * a ----------------------- (m= mass , a = Acceleration)


According to Galileo's model

F = - m * g ------------------------------ ( - because object is accelerating downward)

equating 1 & 2
 m * a = = - m * g

thus  a = -g --------------------------------i.e acceleration will be equal to gravitational force pulling the object down word with 10 m/s^2

Now lets consider an object of mass (m) who is falling towards earth having mass (M).
Now according to newtons gravitational law
the force of attraction between two objects (m &M ) are given by

F = (m * M) * G / r^2

& also we know that object of mass 'm' is moving & is being attracted towards 'M' by certain force & that can be given by

F= m * a

therefore on comparing these  2 equations we have
m * a = (m * M) * G / r^2
Which finally gives

a =  (M * G) / r^2 ---------------------------------------------( Note down here the mass of small object falling to earth is not appearing)

Acceleration of small object is independent of its mass. i.e if there are no. of objects falling towards earth then their acceleration will not depend on their individual masses but it depends on the the other object on which they are falling.
Thus we can say that every object falling on ground will take same time provided they are dropped at same time.