If the distance between two masses is doubled, how does the gravitational force
Practice Questions
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
Questions & Step-by-Step Solutions
If the distance between two masses is doubled, how does the gravitational force between them change?
Correct Answer: 1/4 of the original force
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.
Gravitational Force – The gravitational force between two masses is described by Newton's law of universal gravitation, which states that the force is inversely proportional to the square of the distance between the centers of the two masses.
Inverse Square Law – This law indicates that if the distance between two objects is increased, the gravitational force decreases by the square of the distance increase.
