How does the gravitational force between two objects change if the distance between them is halved?
Practice Questions
1 question
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
According to Newton's law of gravitation, if the distance is halved, the force increases by a factor of 4 (F ∝ 1/r²).
Questions & Step-by-step Solutions
1 item
Q
Q: How does the gravitational force between two objects change if the distance between them is halved?
Solution: According to Newton's law of gravitation, if the distance is halved, the force increases by a factor of 4 (F ∝ 1/r²).
Steps: 6
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.
