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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 ?
Explanation
According to Newton's Universal Law of Gravitation, the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between them, expressed as F = G(m1*m2)/r^2. If the mass of one object is doubled, the force initially doubles (2F). However, the force is also subject to the inverse-square law regarding distance; doubling the distance (2r) results in the force being divided by the square of that factor, which is 4 (1/2^2). Combining these changes, the new force becomes (2 * F) / 4, which simplifies to F/2. Therefore, the net effect of doubling one mass and doubling the distance is that the gravitational force is halved.