If the distance is doubled in the formula for gravitational force, how is the force affected?

If the distance is doubled in the formula for gravitational force, how is the force affected?

• A. It becomes eight times stronger
• B. It becomes one quarter as strong
• C. It becomes twice as strong
• D. It remains unchanged

Answer: (B)

Gravitational force follows an inverse-square law: F is proportional to 1 over the distance squared. So when the distance doubles, the distance squared becomes (2r)^2 = 4r^2. That makes the force drop to one fourth of its original value. Put simply, F' = F/4. For intuition, if the original force were 100 units at distance r, at twice that distance it would be 25 units. This is why the correct description is that the force becomes one quarter as strong.

Gravitational force follows an inverse-square law: F is proportional to 1 over the distance squared. So when the distance doubles, the distance squared becomes (2r)^2 = 4r^2. That makes the force drop to one fourth of its original value. Put simply, F' = F/4. For intuition, if the original force were 100 units at distance r, at twice that distance it would be 25 units. This is why the correct description is that the force becomes one quarter as strong.