Final answer:
The spring constant is calculated as k = F/x. For a force of 4 N causing a stretch of 0.2 cm (0.002 m), the spring constant is 2000 N/m, which does not match the listed options, suggesting an error in the question or options.
Step-by-step explanation:
The spring constant, often denoted by the symbol k, is a measure of the stiffness of a spring. It can be calculated using Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the displacement or stretch (x) from its equilibrium position, expressed as F = kx. To find the spring constant, we rearrange the equation to k = F/x.
In this case, a force of 4 N causes a stretch of 0.2 cm in the spring. Since we need the displacement in meters for the spring constant to be in N/m, we convert 0.2 cm to 0.002 m. Thus, the spring constant k is calculated as:
k = F/x = 4 N / 0.002 m = 2000 N/m
However, the value of 2000 N/m does not match any of the options provided, indicating there might be a misunderstanding in the question or the provided options. The closest answer from the options listed would be choice 1) 20 N/m, but this must be an error as it does not correctly reflect the calculated spring constant.