the gravitational force between 2 objects is 100nhow should the distance between the two objects be changed so that the gravitational force between the two objects be 200n.
Answers
Answer:-
The distance between the two objects should be decreased by √2 times so that the gravitational force between the two objects will be 200N.
Explanation:-
By Newton's Universal Law of Gravitation, we know that :-
F = GMm/r²
Where :-
• F is the gravitational force.
• G is Universal Gravitational Constant.
• M is mass of the 1st body.
• m is mass of the 2nd body
• r is the distance between the bodies.
Case 1 :-
Given that the force bewteen the two objects is 100N. Hence :-
=> 100 = GMm/r² ----(1)
Case 2 :-
Given that, the force in this case is 200N. So, let the new distance of separation be r'. Hence :-
=> 200 = GMm/(r')² -----(2)
On dividing eq.2 by eq.1, we get :-
=> 200/100 = [GMm/(r')²]/[GMm/(r²]
=> 2 = r²/(r')²
=> √2 = √r²/(r')²
=> √2 = r/r'
=> r' = r/√2
Answer:
the distance increased by 1/√2 of the object distance.