Hello students welcome to another chapter of physics the most important and interesting chapter gravitation we start with the first model of gravitation in which will understand the fundamental concept given by Newton that’s the Newton’s gravitational law its statement and explanation let’s start with the Newton’s law of gravitation let’s understand the meaning of it and then define the law now for that let’s consider m1 as a mass of a body a and let’s consider another mass m2 of mass of body b lets say these two masses are separated by some distance R then according to Newton there exists a force of attraction between these two masses and this, this force of attraction between the two material bodies is called as the gravitational force now according to Newton this gravitational force of attraction is directly proportional to the product of the masses m1 m2 and this gravitational forces also inversely proportional to the square of the distance between these two masses if I just accumulate these two personalities I get this gravitational force is proportional to M 1 M 2 upon r square and this will be our fundamental to make a statement of the law now looking at this proportionality it’s very easy to define the law the law goes something like this every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of the mass and inversely proportional to the square of the distance between them if i remove the proportionality and make an equation out of it I’ll have to put a proportionality constant so if we introduce a constant say capital G then the equation becomes F is equal to g* m1* m2 upon r square  now students note this capital G is a very special constant in this case this constant of proportionality is called as universal gravitation constant Remember ok fine let’s discuss some questions related to this let’s see whether you understood this properly the first question gravitational force is directly proportional to the product of mass some of mass division of mass or each of the mass?? I hope you remember the statement a very simple but a very fundamental thing about the law yes the gravitational force is directly proportional to the product of the Masses accordingly the answer  is a . let’s see some more questions another one for you gravitational forces mathematically given as capital F equal to g m1 plus m2 upon r or equal to g m1 m2 upon r or is it g m1 m2 upon R square or is it given as G R squared upon m1 m2 a very fundamental question I hope you remembered answer you remember this slide we just noted it yes the gravitational forces always given us what G m1 m2 upon R Square your answer is in this case see let’s see one more question in the Newton’s law of gravitation what is capital g is it universal gravitation constant is it an acceleration due to gravity or is it a variable or it is just any constant in this case just remember this a very critical thing capital g yes here it is we had done this we understood that capital g is called as the universal gravitational constant it’s a universal constant ok and please remember the second option which says acceleration due to gravity that is nothing but small G which is going to come in the next part of the chapter and don’t get confused between these two things small G and capital g right ok let’s see one more question if somehow the distance between the Sun and earth is doubled then the gravitational force between them will become what now you know gravitational forces inversely proportional to the square of the distance between the two material bodies and inversely proportional means if R increases force F will decrease right so force will decrease means a option and B option cannot be answer because that says doubling and four times not possible so either it is half or one fourth and it’s a very oral mathematical thing F proportional to 1 upon R square if R is getting double then force would become 1 by 2 square times means it will become 1 /4th will understand that in detail if I consider let’s say the new distances R2then R2 will be 2 times r1 we need to find out what is a new force f2 now you know that F is proportional to 1 upon R square so f2 upon F 1 will be R1 upon r 2 the whole square if i put in place of R2 2 times r1 I get on the other side r 1 upon 2 r 1 the whole square canceling R1 1 by 2 the whole square is 1 by 4 that is f2 IS F 1 / 4 so what is a new force it’s one fourth of the initial answer is d clear.