Final answer:
Block B, being heavier, will accelerate downward, pulling Block A upward. This movement is dictated by Newton's laws and the dynamics of a pulley system with frictionless and massless components.
Step-by-step explanation:
When Block B, which is twice as massive as Block A, moves downward, it causes Block A to rise. This is a classical physics problem involving Newton's laws and the principles of tension and acceleration in a pulley system. In a frictionless and massless pulley setup, when one block goes down, the other block ascends with a motion directly connected to Block B's downward motion due to the conservation of energy and Newton's third law, which states that for every action, there's an equal and opposite reaction. The heavier block (Block B) will accelerate downwards, pulling Block A upwards, with an acceleration that can be calculated from the differences in their weight (mass times gravitational acceleration).
If the masses are m and 2m for blocks A and B, respectively, and B is on the lower side, it will descend due to the force of gravity acting more strongly on it. As per Newton's second law (F = ma), the net force on the system and the acceleration of both blocks can be calculated. Since Block B's mass is greater (2m), it will move downward and cause Block A to move the same distance upward but with half the acceleration due to the difference in mass.