Final answer:
The displacement of blocks connected to a spring is inversely proportional to the spring constant, following Hooke's law where the restoring force is directly proportional to the displacement.
Step-by-step explanation:
The displacement of blocks connected to a spring is related to the spring constant k in a system where Hooke's law is applicable. According to Hooke's law, the restoring force (F) exerted by the spring is directly proportional to the displacement (x). The force constant k is a measure of the rigidity or stiffness of the spring system. Since F = -kx, when we solve for the displacement x, we find x = -F/k. This means that the displacement is inversely proportional to the spring constant k. If we look into the context of masses attached to the spring, we'll find that a heavier mass (2m compared to m) leads to more displacement for the same amount of force applied if the spring constant is kept constant.
However, inversely, if the displacement is to remain the same for different masses, a larger spring constant would be required for the heavier mass. Therefore, the displacement is inversely proportional to the spring constant, and since the spring constant has units of N/m, we do not need to involve roots in the relationship. Hence, the correct answer is b. The displacement is inversely proportional to the square root of the spring constant.