If the distance between two objects is increased by two times, the gravitational force between them will
[amp_mcq option1=”remain same” option2=”increase by two times” option3=”decrease by two times” option4=”decrease by four times” correct=”option4″]
This question was previously asked in
UPSC CDS-2 – 2020
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.