If the distance between two masses is halved, how does the gravitational force change?
Practice Questions
1 question
Q1
If the distance between two masses is halved, how does the gravitational force change?
It becomes four times stronger
It becomes twice stronger
It remains the same
It becomes half as strong
If the distance is halved, the force becomes 1/(1/2)^2 = 4 times stronger.
Questions & Step-by-step Solutions
1 item
Q
Q: If the distance between two masses is halved, how does the gravitational force change?
Solution: If the distance is halved, the force becomes 1/(1/2)^2 = 4 times stronger.
Steps: 9
Step 1: Understand that gravitational force depends on the distance between two masses.
Step 2: Recall 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: If the distance (r) is halved, 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).
Step 6: Rewrite the force formula: F' = G * (m1 * m2) / (r^2 / 4).
Step 7: This can be rewritten as F' = G * (m1 * m2) * (4 / r^2).
Step 8: Notice that F' = 4 * (G * (m1 * m2) / r^2), which means the new force (F') is 4 times the original force (F).
Step 9: Conclude that if the distance is halved, the gravitational force becomes 4 times stronger.
