The gravitational force between two objects is 10N, what is the new value of the force if the distance between them is halved?

Analyze the question The gravitational force between two masses is 10 N. We need the new force when the distance between them is halved, with the masses unchanged.

Concept Newton's law of universal gravitation:

F = Gm₁m₂ / r²

The force is inversely proportional to the square of the distance (F ∝ 1/r²).

Solution

Initial force: F₁ = Gm₁m₂ / r² = 10 N

New distance: r₂ = r/2

F₂ = Gm₁m₂ / (r/2)² F₂ = Gm₁m₂ / (r²/4) F₂ = 4 × (Gm₁m₂ / r²) F₂ = 4 × 10 = 40 N

Answer: C. 40 N

Tip For inverse-square laws (gravity, Coulomb's law, light intensity), remember this rule:

• Distance halved → force × 4
• Distance doubled → force ÷ 4
• Distance tripled → force ÷ 9

The factor applied to the force is the square of the factor applied to the distance, inverted. Many students wrongly answer 20 N by treating the relationship as simple inverse proportion. Always check whether it is r or r² in the formula.