The force of gravity is an inverse square law. This means that, if you double the distance between two large masses, the gravitational force between them

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BlackTom AI · Accepted Answer

The question states a fundamental property of gravity: it follows an inverse square law. This means that the gravitational force F between two masses is proportional to 1/r^2, where r is the distance between the masses.

If you double the distance from r to 2r, the new force F' is proportional to 1/(2r)^2, which simplifies to 1/(4r^2). This shows the force has become one quarter of its original value, or equivalently it has weakened by a factor of 4.

To see this another way: since F ∝ 1/r^2, the ratio F'/F = (1/(2r)^2) / (1/r^2) = (1/4r^2) / (1/r^2) = 1/4. Therefore, doubling the separation results in a fourfold decrease in the force.

A common misconception would be to think the force halves or reduces linearly with distance. However, the inverse square dependence means distance changes have quadratic effects, not linear ones. If the distance were tripled, the force would drop by a factor of 9, not 3, illustrating the squared relationship.

Given the prompt, the provided statement—"weakens by a factor of 4" when distance is doubled—precisely reflects the 1/r^2 dependence of gravitational force.

COS SPR 25 class 2 Jan 30 Test1 (USE GOOGLE CHROME)

The force of gravity is an inverse square law. This means that, if you double the distance between two large masses, the gravitational force between them

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