If two objects are placed in space, how does the gravitational force between the
Practice Questions
Q1
If two objects are placed in space, how does the gravitational force between them change if the distance is halved?
It becomes half
It becomes double
It becomes four times stronger
It remains the same
Questions & Step-by-Step Solutions
If two objects are placed in space, how does the gravitational force between them change if the distance is halved?
Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Know that the formula for gravitational force (F) is F = G * (m1 * m2) / r^2, where 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 distance (r) is halved, it means we replace r with r/2 in the formula.
Step 4: Substitute r/2 into the formula: F = G * (m1 * m2) / (r/2)^2.
Step 5: Simplify (r/2)^2 to get (r^2 / 4). So, the formula becomes F = G * (m1 * m2) / (r^2 / 4).
Step 6: When you divide by (r^2 / 4), it is the same as multiplying by 4. So, F = 4 * (G * (m1 * m2) / r^2).
Step 7: This shows that the gravitational force increases by a factor of 4 when the distance is halved.
