Final answer:
The acceleration of the more massive box on a frictionless surface, when a force F is applied to it, is given by F/(5m) since the total mass of the system is 5m.
Step-by-step explanation:
The question is asking for the acceleration of the more massive box which is in contact with a smaller box on a frictionless surface. If we consider a force F applied to the two-box system, we must realize that this force will accelerate both boxes equally on a frictionless surface. Since the system consists of masses m and 4m, the total mass is 5m. According to Newton's second law, F = ma, where m is the mass and a is the acceleration. To find the acceleration a of the system (and therefore of the more massive box), we can rearrange the equation to a = F/m. In this case, the total mass m is 5m (the sum of m and 4m), so the acceleration of the system is given by a = F/(5m).