If the distance between two masses is doubled, how does the gravitational force between them change?
Practice Questions
1 question
Q1
If the distance between two masses is doubled, how does the gravitational force between them change?
It becomes four times weaker
It becomes twice as strong
It remains the same
It becomes half as strong
According to the inverse square law, if the distance is doubled, the force becomes 1/(2^2) = 1/4 of the original force.
Questions & Step-by-step Solutions
1 item
Q
Q: If the distance between two masses is doubled, how does the gravitational force between them change?
Solution: According to the inverse square law, if the distance is doubled, the force becomes 1/(2^2) = 1/4 of the original force.
Steps: 7
Step 1: Understand that gravitational force depends on the distance between two masses.
Step 2: Know that the formula for gravitational force is F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
Step 3: If the distance (r) is doubled, it becomes 2r.
Step 4: Substitute 2r into the formula: F' = G * (m1 * m2) / (2r)^2.
Step 5: Simplify (2r)^2 to get 4r^2, so the new force is F' = G * (m1 * m2) / 4r^2.
Step 6: Compare the new force F' to the original force F: F' = 1/4 * F.
Step 7: Conclude that if the distance is doubled, the gravitational force becomes 1/4 of the original force.
