What happens to the gravitational force between two objects if the mas

What happens to the gravitational force between two objects if the mass of one object is doubled and the distance between them is also doubled ?

The force would remain the same

The force would be doubled

The force would be halved

The force would increase by a factor of 4

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CDS-1 – 2022

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According to Newton’s Law of Gravitation, the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. Doubling one mass increases the force by a factor of 2. Doubling the distance increases the distance squared by a factor of 4 (2^2), which decreases the force by a factor of 4. The combined effect is a force that is (2 * 1) / 4 = 1/2 times the original force.

Newton’s Law of Gravitation is given by F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

If the mass of one object is doubled (m1′ = 2m1) and the distance is doubled (r’ = 2r), the new force F’ is given by F’ = G * (m1′ * m2) / (r’)^2 = G * (2m1 * m2) / (2r)^2 = G * (2m1 * m2) / (4r^2) = (2/4) * G * (m1 * m2) / r^2 = (1/2) * F. Thus, the force would be halved.

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