What happens to the force between two objects, if
(i) The mass of one object is doubled?
(ii) The distance between the objects is doubled and tripled?
(iii) The masses of both objects are doubled?
Answers
Answer:
I) From the relationship, If the mass of one object (say body 1) is doubled, then Thus, the gravitational force between the two objects gets doubled. ... If the masses of both the objects are doubled, then Thus, the gravitational force between the two objects becomes 4 times.
II) When distance between objects is doubled, force of attraction will become 122=14 times i.e. will become one-fourth. When distance between objects is halved, force of attraction will become 1(12)2=114=4 times i.e. will become four times.
III) If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.
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[Case 1:-]
By Newton's Universal Law of gravitation;-
=>F=GMm/r² ----(1)
ATQ,if mass of one object is doubled,the new force:-
=>F'=G2Mm/r². ---(2)
Now,on dividing eq.2 by eq.1,we get:-
=>F'/F=(G2Mm/r²)/(GMm/r²)
=>F'/F=2
=>F'=2F
Thus,if mass of one object is doubled ,the force is also doubled i.e.2F.
[Case 2:-]
=>F=GMm/r². ---(1)
ATQ,if distance is doubled,the new force:-
=>F=GMm/(2r)²
=>F'=GMm/4r². --(2)
Now,on dividing eq.2 by eq.1,we get:-
=>F'/F=(GMm/4r²)/(GMm/r²)
=>F'/F=1/4
=>F'=F/4
Thus,if distance between the objects is doubled,the force becomes F/4
Similarly,if the distance between the objects is tripled,the force will become F/9.
[Case 3:-]
=>F=GMm/r². ---(1)
ATQ,if masses of both the objects are doubled,then new force:-
=>F=G2M2m/r²
=>F'=G4Mm/r². ---(2)
Now,on dividing eq.2 by eq.1 we get:-
=>F'/F=(G4Mm/r²)/(GMm/r²)
=>F'/F=4
=>F'=4F
Thus,if masses of both the objects are doubled,the force becomes four times i.e. 4F.