If two objects are moved to a distance of half their original separation, how do
Practice Questions
Q1
If two objects are moved to a distance of half their original separation, how does the gravitational force change?
It becomes four times stronger
It becomes twice stronger
It remains the same
It becomes half as strong
Questions & Step-by-Step Solutions
If two objects are moved to a distance of half their original separation, how does the gravitational force change?
Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Recall the formula for gravitational force: F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
Step 3: If the original distance (r) is halved, the new distance becomes r/2.
Step 4: Substitute the new distance into the formula: F' = G * (m1 * m2) / (r/2)^2.
Step 5: Simplify the equation: (r/2)^2 = r^2 / 4, so F' = G * (m1 * m2) / (r^2 / 4).
Step 6: This can be rewritten as F' = G * (m1 * m2) * 4 / r^2, which shows that F' = 4 * F.
Step 7: Conclude that if the distance is halved, the gravitational force becomes 4 times stronger.
