In basic mechanics, a spring that shows a linear relationship between the force applied and its extension is an example of which fundamental physical law?

Introduction / Context:
Springs are very common mechanical elements found in pens, vehicles, machines, and scientific instruments. In introductory physics, they are used as a standard example to illustrate how force and extension can be related by a simple linear law over a certain range. This law is known as Hookes law and is one of the earliest and most important empirical laws in mechanics. The question asks you to connect the everyday example of a spring with the correct named physical law that governs its behaviour for small deformations.

Given Data / Assumptions:
• We are dealing with an ideal elastic spring within its elastic limit. • The spring shows a proportional relationship between stretching force and extension. • The options mention several laws, including Hookes law and Newton laws of motion. • No information suggests plastic deformation or permanent change in length.

Concept / Approach:
Hookes law states that, for an ideal spring within its elastic limit, the restoring force F is proportional to the extension x, usually written as F = k * x, where k is the spring constant. This is exactly the typical behaviour of a standard helical spring in lab experiments. Newton laws of motion deal with how forces affect motion, inertia, and action reaction pairs, but they do not specifically describe how the extension of a spring depends on the applied load. The law of conservation of mass is a separate principle from mechanics of springs. Therefore, the correct law that a simple spring demonstrates is Hookes law.

Step-by-Step Solution:
Step 1: Recall that stretching a spring produces a restoring force that opposes the deformation. Step 2: In experiments, when you double the load on a spring within limits, the extension approximately doubles too. Step 3: This direct proportionality between force and extension is written as F = k * x. Step 4: This relationship is known as Hookes law and defines the spring constant k. Step 5: Newtons laws of motion describe dynamics of bodies but do not give this specific linear force extension rule. Step 6: Therefore the behaviour of a normal elastic spring is an example of Hookes law.

Verification / Alternative check:
You can verify the connection by looking into any standard school or college physics textbook. The chapter on elasticity or simple harmonic motion will show a diagram of a spring with weights attached and will clearly state Hookes law as the governing relationship. Graphs of force versus extension for a spring are straight lines through the origin in the elastic region, exactly as Hookes law predicts. By contrast, Newtons first law discusses motion without net force, Newtons third law refers to action and reaction pairs, and conservation of mass is related to matter and chemistry rather than elasticity. This confirms that the spring example is specifically tied to Hookes law.

Why Other Options Are Wrong:
Option A, Newtons third law, states that every action has an equal and opposite reaction, which is a fundamental idea but does not describe how far the spring extends for a given load. Option C, Newtons first law, is about inertia and motion in the absence of net force, which is not directly about springs. Option D, conservation of mass law, belongs primarily to chemistry and thermodynamics and does not explain the mechanical response of springs to applied forces. Therefore, none of these options correctly represents the specific force extension relation seen in springs.

Common Pitfalls:
Many students confuse Hookes law with Newtons laws because all of them involve forces. Another common mistake is to assume that Hookes law holds for any amount of stretching. In reality, Hookes law is valid only within the elastic limit of the material, and if the spring is stretched too far, the relationship becomes non linear and may result in permanent deformation. It is important to remember both the name of the law and its conditions of validity when answering similar questions.

Final Answer:
The correct choice is Hookes law relating force and extension, because a spring whose extension is proportional to the applied force is a classic example of Hookes law in mechanics.