If the distance between two masses is doubled, how does the gravitational force change?
Practice Questions
1 question
Q1
If the distance between two masses is doubled, how does the gravitational force change?
It becomes four times weaker
It becomes twice weaker
It remains the same
It becomes four times stronger
According to the inverse square law, if the distance is doubled, the force becomes 1/(2^2) = 1/4, or four times weaker.
Questions & Step-by-step Solutions
1 item
Q
Q: If the distance between two masses is doubled, how does the gravitational force change?
Solution: According to the inverse square law, if the distance is doubled, the force becomes 1/(2^2) = 1/4, or four times weaker.
Steps: 8
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: Calculate (2r)^2, which equals 4r^2.
Step 6: Now the formula looks like this: F = G * (m1 * m2) / 4r^2.
Step 7: Compare this new force to the original force: the new force is 1/4 of the original force.
Step 8: Conclude that if the distance is doubled, the gravitational force becomes four times weaker.
