Two bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M each are placed R/2 a distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies in the second system will be

According to Newton's law of universal gravitation, the force (F) between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In the first system, the force is F = G(M * M) / R². In the second system, the masses are doubled to 2M each, and the distance is halved to R/2. Substituting these values into the formula, the new force F' = G(2M * 2M) / (R/2)². This simplifies to F' = G(4M²) / (R²/4). By moving the denominator of the distance term to the numerator, we get F' = 16 * (GM² / R²). Since the original force F was (GM² / R²), the new force is exactly 16 times the original force (16 F).