Final answer:
Both balls fall from the same height, so despite having different masses (m and 4m), they hit the ground with the same velocity. However, since kinetic energy depends on mass, Ball 2, with mass 4m, will have four times more kinetic energy than Ball 1 upon impact, due to its greater mass.
Step-by-step explanation:
The question involves understanding the concept of kinetic energy in the context of gravitational potential energy conversion as two balls fall from the same height without air resistance. According to the conservation of energy principle, potential energy (PE) is converted into kinetic energy (KE) as the balls fall. Given that both balls are dropped from the same height, they will both have the same amount of gravitational potential energy to start with, which is given by the formula PE = m × g × h, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height. Since there is no air resistance, potential energy will be completely converted into kinetic energy just before they hit the ground. Therefore, the kinetic energy for each ball can be found using the formula KE = 0.5 × m × v2, where 'v' is the velocity just before impact.
As both balls fall from the same height without any air resistance, they will both reach the ground with the same velocity, because the acceleration due to gravity is the same for both. Thus, the velocity term in the kinetic energy formula will be equal for both balls. Since ball 2 has a mass of '4m' and ball 1 has a mass of 'm', and the velocity squared term is the same for both, it follows that ball 2 will have four times the kinetic energy of ball 1 just before impact. Therefore, the correct answer is: b) Ball 2 has more kinetic energy than Ball 1.