The force of gravity is more sensitive to changes in distance or mass?

The force of gravity is more sensitive to changes in distance or mass?

• A. Mass
• B. Both equally
• C. Distance
• D. Gravity not sensitive to either

Answer: (C)

Gravitational force depends on distance as an inverse square, F ∝ 1/r^2, and on each mass linearly, F ∝ m1 m2. That means small changes in distance produce larger relative changes in the force than the same small changes in mass. For tiny changes, the fractional change in force from distance is about twice the fractional change in distance itself: dF/F ≈ -2(dr/r). In contrast, the fractional change from changing mass is simply dF/F ≈ dm/m. So distance has a stronger effect on gravity than mass. Concrete intuition helps: doubling the distance makes gravity drop to one quarter (a 75% decrease), while doubling a mass only doubles the gravitational pull (a 100% increase). Halving the distance multiplies gravity by four, whereas halving the mass halves gravity. Therefore, gravity is more sensitive to changes in distance than to changes in mass.

Gravitational force depends on distance as an inverse square, F ∝ 1/r^2, and on each mass linearly, F ∝ m1 m2. That means small changes in distance produce larger relative changes in the force than the same small changes in mass. For tiny changes, the fractional change in force from distance is about twice the fractional change in distance itself: dF/F ≈ -2(dr/r). In contrast, the fractional change from changing mass is simply dF/F ≈ dm/m. So distance has a stronger effect on gravity than mass.

Concrete intuition helps: doubling the distance makes gravity drop to one quarter (a 75% decrease), while doubling a mass only doubles the gravitational pull (a 100% increase). Halving the distance multiplies gravity by four, whereas halving the mass halves gravity. Therefore, gravity is more sensitive to changes in distance than to changes in mass.