Newton's universal law of gravitation is expressed mathematically as
`F=(Gm_(1)m_(2))/d^(2)`
Answer the following the question based on this law:
(i) what is represented by `m_(1),m_(2)` and d?
(ii) what is G called?
(iii) what is the meaning of the world 'universal' in this law?
(iv) Gravitational force between any two ordinary objects is really weak. why?
(v) why you or your friend sitting near you do not move towards each other due to gravitation force of attraction?
(vi) Though gravitational force is the weakest force in nature, yet it is responsible for holding our solar system.why?
(vii) will gravitational force of attraction between two bodies change when they are placed same distance apart (i) on earth (ii) on moon?
(viii) how will gravitational force change between two bodies when distance between them is halved?
(ix) masses of each of two bodies are doubled. how should the distance between them be changed to keep the gravitational force constant?

Explanation

(i) `m_(1)m_(2)` are masses of two bodies and d is distance between their centres.
(ii) G is called universal gravitational constant.
(iii) 'universal' in this law means that the law applies equally to any two objects in the universe, whatever be their size, shape, mass, distance ect.
(iv)This is because `G=6.67xx10^(11)Nm^(2)kg^(2),` which is really small.
(v) This is because masses of G is too small. the gravitational pull is too weak to overcome the force of friction opposing the motion. (vi) This is because masses of celestial bodies in our solar system are really large. the gravitational force `(Fprop m_(1)m_(2))` because significant.
(vii) No,it will not change. (viii) As `Fprop(1)/(d^(2))`, therefore, when d is halved, F become 4 times.
(ix)As `F=(Gm_(1)m_(2))/d^(2)`, and numerator becomes 4 time, therefore to keep F unchanged, `d^(2)` should become 4 times or d should be made 2 times.