Question at position 19 Which of the following statements about the force of gravity is FALSE?its strength decreases as one over the square of the distance.it is a universal force, which acts everywhere in space.its strength is inversely proportional to the mass of an object.it causes the paths of the planets to be ellipses.it causes object to fall near the surface of the Earth.Clear my selection

Question

BlackTom AI · Accepted Answer

Newton’s law of universal gravitation states F = G m1 m2 / r^2, so the force between two point masses is proportional to the product of their masses and falls off as the inverse square of the separation.

1) Relevant knowledge points and concepts
- Newton’s law of gravitation: F = G m1 m2 / r^2 (G is the gravitational constant).
- Gravitational field/acceleration near a mass M: g = GM / r^2, and an object’s weight is mg.
- Inverse-square central forces produce conic-section orbits (Kepler’s laws follow from Newtonian gravity).

2) Step-by-step reasoning
- From F = G m1 m2 / r^2, the dependence on distance is 1/r^2, so statement “its strength decreases as one over the square of the distance” is true.
- The law applies to all masses everywhere in space (universal), so “it is a universal force, which acts everywhere in space” is true.
- The force formula shows F ∝ m1 m2 (direct proportionality to mass), not inversely proportional to mass, so “its strength is inversely proportional to the mass of an object” is inconsistent with the formula.
- For a small mass m orbiting a large mass M, acceleration a = F/m = G M / r^2 — independent of the orbiting mass — and for an inverse-square central force, orbital solutions are ellipses (Kepler’s first law), so “it causes the paths of the planets to be ellipses” is true.
- Near Earth’s surface, g ≈ GM_earth / R_earth^2 gives objects accelerating downward, so “it causes object to fall near the surface of the Earth” is true.

3) Calculations / intermediate steps
- F = G m1 m2 / r^2 (explicitly shows proportionality to masses and inverse-square distance).
- a = F/m = G M / r^2 (shows acceleration independent of the small mass).

4) Why the correct answer is correct
Because the correct answer option contradicts the fundamental formula: gravity’s strength is directly proportional to mass (product of masses), not inversely proportional.

5) Why the other options are incorrect (brief)
- Option 1 (inverse-square): correct by the 1/r^2 term.
- Option 2 (universal): correct—applies everywhere.
- Option 4 (ellipses): correct—Newtonian gravity yields Keplerian ellipses for bound orbits.
- Option 5 (fall near Earth): correct—gravity produces downward acceleration near Earth.

6) Conclusion
The false statement is “its strength is inversely proportional to the mass of an object.” This matches the provided answer.

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