The gravitational force between two objects, [math: M1] M_1 and [math: M2] M_2 , a distance of [math: R] apart is found to be [math: F] . Both masses were multiplied by a factor of 12, and the distance between them by a factor of 2.What would be the ratio of the new force compared to the initial force [math: FnewFinitial] \frac{ F_{new} }{ F_{initial} } ?

Question

The gravitational force between two objects, [math: M1] M_1 and [math: M2] M_2 , a distance of [math: R] apart is found to be [math: F] . Both masses were multiplied by a factor of 12, and the distance between them by a factor of 2.What would be the ratio of the new force compared to the initial force [math: FnewFinitial] \frac{ F_{new} }{ F_{initial} } ?

BlackTom AI · Accepted Answer

We start from the gravitational force law: F ∝ (M1 * M2) / R^2, where F is proportional to the product of the masses divided by the square of the distance.

Option a: 0.17. This is far from the calculated ratio. If masses increase and distance decreases as given, the force should increase, not drop to a fraction around 0.17. The square of the distance in the denominator grows only if distance increases; here distance is reduced, which would move the ratio upward, not downward to 0.17.

Option b: 6.00. To get a factor of 6, one would need different scaling effects. In this problem, the masses are multiplied by 12 (factor 144 in the product M1*M2), and the distance is multiplied by 2 (factor 4 in the denominator). The net factor is 144/4 = 36, not 6. So this option misunderstands how the two scaling factors combine.

Option c: 6.00. This is essentially a repeat of option b with the same incorrect reasoning. It does not reflect the correct combination of mass and distance scaling. The actual ratio is not 6, given the 12× mass and 2× distance changes.

Option d: 36.00. This matches the proper combination: increasing both masses by a factor of 12 gives a factor of 12 × 12 = 144 in the numerator, while increasing the distance by a factor of 2 gives a factor of 2^2 = 4 in the denominator. The ratio becomes 144 / 4 = 36, so F_new is 36 times the initial force.

Overall, by applying F ∝ M1 M2 / R^2 and substituting the given multipliers, the correct ratio is 36, while the other options reflect common misapplications of the scaling rules or arithmetic mistakes.

MUF0121 Physics Unit 1 - Semester 2, 2025

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