What happens to the gravitational force between two masses if the distance between them is tripled?
Practice Questions
1 question
Q1
What happens to the gravitational force between two masses if the distance between them is tripled?
It triples
It becomes one-third
It becomes one-ninth
It remains the same
The gravitational force is inversely proportional to the square of the distance. If the distance is tripled, the force becomes 1/(3^2) = 1/9 of the original force.
Questions & Step-by-step Solutions
1 item
Q
Q: What happens to the gravitational force between two masses if the distance between them is tripled?
Solution: The gravitational force is inversely proportional to the square of the distance. If the distance is tripled, the force becomes 1/(3^2) = 1/9 of the original force.
Steps: 9
Step 1: Understand that gravitational force depends on the masses and the distance between them.
Step 2: Remember 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, and r is the distance between them.
Step 3: Note that the gravitational force is inversely proportional to the square of the distance (r). This means that if the distance increases, the force decreases.
Step 4: If the distance (r) is tripled, it becomes 3r.
Step 5: Substitute 3r into the formula: F' = G * (m1 * m2) / (3r)^2.
Step 6: Calculate (3r)^2, which is 9r^2.
Step 7: Now the new force (F') is F' = G * (m1 * m2) / 9r^2.
Step 8: Compare the new force (F') to the original force (F): F' = (1/9) * F.
Step 9: Conclude that if the distance is tripled, the gravitational force becomes 1/9 of the original force.
