Final answer:
The question requires understanding and applying Newton's laws of motion to a two-mass pulley system to find the acceleration of the system and tension in the rope.
Step-by-step explanation:
The question relates to classical mechanics in Physics and involves the dynamics of a system of masses, a pulley, and tension in a string. It's primarily focused on understanding Newton's laws of motion and their application to pulley systems. To solve problems like these, we generally utilize free body diagrams and equations of motion.
For instance, to find the acceleration of a system of two masses connected by a massless rope over a frictionless pulley, we first need to identify the forces acting on each mass. For the mass hanging off the table, the only forces are gravity and the tension in the string. For the mass on the table, the tension in the string is the only force causing acceleration. Using Newton's second law, F=ma, where F is the net force on the mass, m is the mass, and a is the acceleration, we can set up two equations, one for each mass, and solve them simultaneously to find both the acceleration of the system and the tension in the string.