According to Newton's Law of Universal Gravitation, the force (F) between two objects with masses m₁ and m₂ separated by a distance (r) is given by F = G(m₁m₂)/r², where G is the gravitational constant. The force is inversely proportional to the square of the distance between the objects. If the distance is increased by two times (r' = 2r), the new force (F') will be F' = G(m₁m₂)/(r')² = G(m₁m₂)/(2r)² = G(m₁m₂)/(4r²) = (1/4) G(m₁m₂)/r² = (1/4) F. Thus, the force decreases to one-fourth of its original value.
If the distance between two objects is increased by two times, the gravitational force between them will
Asked in UPSC CDS 2 2020 · Topic: Mechanics (Gravitation and Central Force Motion (Kepler's Laws))
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