A 4-kg mass and a 10-kg mass are acted on by the same constant net force during the same amount of time. Both masses are at rest before the force is applied. The 10-kg mass moves a distance X₁ and the 4-kg mass moves a distance X₂ as a result. Which one of the following statements is true? A) The ratio X₁/X₂ is equal to 5/2. B) The ratio X₁/X₂ is equal to (5/2)². C) The ratio X₁/X₂ is equal to (2/5)². D) The ratio X₁/X₂ is equal to 2/5. E) X₁ is equal to X₂.

Question

Quizplus · Accepted Answer

The acceleration is inversely proportional to mass (a = F/m). Therefore, the 4-kg mass will have a greater acceleration than the 10-kg mass. Since both masses are acted upon for the same time, the distance moved is proportional to the square of the acceleration. Thus, the ratio of distances is inversely proportional to the ratio of masses, squared: (m2/m1)^2 = (4/10)^2 = (2/5)^2.

A 4-Kg Mass and a 10-Kg Mass Are Acted on by the Same