If the distance between two masses is halved, how does the gravitational force between them change?
Practice Questions
1 question
Q1
If the distance between two masses is halved, how does the gravitational force between them change?
It remains the same
It doubles
It quadruples
It halves
F = G * (m1 * m2) / r², if r is halved, F increases by a factor of 4.
Questions & Step-by-step Solutions
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Q
Q: If the distance between two masses is halved, how does the gravitational force between them change?
Solution: F = G * (m1 * m2) / r², if r is halved, F increases by a factor of 4.
Steps: 7
Step 1: Understand the formula for gravitational force, which is F = G * (m1 * m2) / r².
Step 2: Identify the variables in the formula: F is the gravitational force, G is the gravitational constant, m1 and m2 are the two masses, and r is the distance between them.
Step 3: Note that if the distance r is halved, it means 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 the equation: (r/2)² = r²/4, so F = G * (m1 * m2) / (r²/4).
Step 6: When you divide by r²/4, it is the same as multiplying by 4: F = G * (m1 * m2) * 4 / r².
Step 7: This shows that the new gravitational force F is 4 times the original force when the distance is halved.
