Final answer:
The kinetic energy of the marble with mass 2m is greater when it reaches the ground because its initial gravitational potential energy is twice that of the marble with mass m, and both convert their entire potential energy into kinetic energy during the fall.
Step-by-step explanation:
When two marbles of masses m and 2m are dropped from a height h, they will each convert their gravitational potential energy completely into kinetic energy when they reach the ground (ignoring air resistance and assuming acceleration due to gravity, g, is constant). According to the principle of conservation of energy, the potential energy (PE) at the height h for each marble will be PE = mgh for the marble of mass m and PE = 2mgh for the marble of mass 2m. Because the potential energy is wholly converted to kinetic energy (KE), we can infer that the kinetic energies of both marbles at the ground will be equal to their respective potential energies at height h, hence KE1 = mgh and KE2 = 2mgh.
Since KE2 is twice that of KE1, we can conclude that the kinetic energy of the marble with mass 2m is greater when it reaches the ground. Therefore, the correct answer is b) The kinetic energy of the marble with mass 2m is greater.