If the distance between two masses is doubled, the gravitational force becomes:

Question

If the distance between two masses is doubled, the gravitational force becomes:

1. A. Double
2. B. Four times
3. C. Half
4. D. One-fourth (Correct answer)

Correct Answer

Option D — One-fourth

Detailed Solution & Explanation

The correct answer is One-fourth.

Key Points

• This uses Newton's law of universal gravitation, which states that the gravitational force between two masses is inversely proportional to the square of the distance between them:
• F = G·m₁·m₂ / r².
• If the distance r is doubled (becomes 2r), the denominator becomes (2r)² = 4r², so the force becomes:
• F' = G·m₁·m₂ / 4r² = F/4 — that is one-fourth of the original.
• because of the inverse-square law, doubling the distance divides the force by 4, tripling it divides the force by 9, and halving it multiplies the force by 4. The same inverse-square rule governs electrostatic force, light intensity and sound intensity.

Exam Tip

• remember the pattern — the force scales as 1/r², so any factor change k in distance changes the force by a factor 1/k².