Which law describes an equation inversely proportional to distance squared?

Which law describes an equation inversely proportional to distance squared?

• A. Inverse square law
• B. Linear law
• C. Direct proportion law
• D. Quadratic law

Answer: (A)

This question tests how a quantity can fall off with distance when it follows an inverse-square relationship. In an inverse-square law, the strength or intensity diminishes with the square of the distance because the same amount spreads over the surface of a sphere whose area grows as r^2. That means the quantity is proportional to 1 divided by the distance squared. So if you double the distance, the value becomes one quarter of what it was; if you triple the distance, it becomes one ninth, and so on. This pattern shows up in real-world things like light intensity from a point source, or gravitational and electric forces between two objects. The other options describe different kinds of dependencies. A linear or direct proportion would mean the quantity grows with distance, not shrinks. A quadratic relation would mean the quantity grows with the square of the distance, not its inverse. Therefore, the inverse-square law is the description that matches “an equation inversely proportional to distance squared.”

This question tests how a quantity can fall off with distance when it follows an inverse-square relationship. In an inverse-square law, the strength or intensity diminishes with the square of the distance because the same amount spreads over the surface of a sphere whose area grows as r^2. That means the quantity is proportional to 1 divided by the distance squared.

So if you double the distance, the value becomes one quarter of what it was; if you triple the distance, it becomes one ninth, and so on. This pattern shows up in real-world things like light intensity from a point source, or gravitational and electric forces between two objects.

The other options describe different kinds of dependencies. A linear or direct proportion would mean the quantity grows with distance, not shrinks. A quadratic relation would mean the quantity grows with the square of the distance, not its inverse. Therefore, the inverse-square law is the description that matches “an equation inversely proportional to distance squared.”