How does the gravitational force between two objects change if the distance betw
Practice Questions
Q1
How does the gravitational force between two objects change if the distance between them is halved?
It doubles
It quadruples
It remains the same
It halves
Questions & Step-by-Step Solutions
How does the gravitational force between two objects change if the distance between them is halved?
Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Remember Newton's law of gravitation, which states that the force (F) is inversely proportional to the square of the distance (r) between the objects: F ∝ 1/r².
Step 3: If the distance (r) is halved, we can express this as r/2.
Step 4: Substitute r/2 into the formula: F ∝ 1/(r/2)².
Step 5: Simplify the equation: F ∝ 1/(r²/4) = 4/r².
Step 6: This shows that the gravitational force increases by a factor of 4 when the distance is halved.
Newton's Law of Gravitation – The gravitational force between two objects is inversely proportional to the square of the distance between them (F ∝ 1/r²).
