In elasticity, the statement that the strain produced in a body is directly proportional to the stress applied on it, within the elastic limit, is known as ________.

Introduction / Context:
When forces act on a solid body, it deforms. For small deformations, there is a simple linear relationship between the stress applied and the resulting strain, as long as the material remains within its elastic limit. This relationship is a cornerstone of the theory of elasticity and is commonly stated as stress is directly proportional to strain. The law that describes this behaviour has a specific name that students must remember.

Given Data / Assumptions:

• We are dealing with elastic deformation of materials where they return to original shape once the load is removed.
• Within the elastic limit, the material follows a linear stress strain relationship.
• The statement refers to strain being directly proportional to stress.
• Several laws with different names are given in the options, some from other areas of physics.

Concept / Approach:
The law describing linear proportionality between stress and strain is known as Hookes law, named after the scientist Robert Hooke. In mathematical form it is often written as stress proportional to strain or stress = E * strain, where E is Youngs modulus. This relationship holds only within the elastic limit; beyond that, the material may deform plastically and not obey Hookes law. Dollar law and Miller law are not standard names in elasticity, and Kepler laws belong to planetary motion, not material deformation.

Step-by-Step Solution:
Step 1: Recall the standard statement in elasticity: within the elastic limit, stress is directly proportional to strain.Step 2: Remember that this fundamental relationship is known as Hookes law.Step 3: Note that in formula form, stress = E * strain, where E is Youngs modulus.Step 4: Recognise that Dollar law and Miller law are not standard physics laws associated with elasticity.Step 5: Recognise that Kepler laws describe planetary motion and orbits around the sun.Step 6: Conclude that the correct name for the law relating stress and strain is Hookes law.

Verification / Alternative check:
Physics and engineering textbooks on strength of materials always introduce Hookes law early in the discussion of elastic behaviour. Stress strain graphs show a straight line region from the origin up to the proportional limit. This linear section represents Hookes law region. The term is widely used in mechanics, civil engineering, mechanical engineering and materials science to describe how materials behave under small loads. No other law name in the options is used in this context, which confirms Hookes law is the correct choice.

Why Other Options Are Wrong:
Dollar law and Miller law do not correspond to any major principle in basic physics related to elasticity; they are distractor names. Kepler laws describe the motion of planets and satellites, such as that planets sweep out equal areas in equal times, and have nothing to do with stress or strain. Therefore, these options do not match the definition in the question.

Common Pitfalls:
Some learners may confuse Hookes law with Youngs modulus or think that Hookes law is simply F = k * x for springs. In fact, F = k * x is a specific application of Hookes law to springs, where k is the spring constant. The more general form relates stress and strain in materials. Another mistake is to think Hookes law applies beyond the elastic limit, which is not true. Remember that the direct proportionality holds only as long as the material behaves elastically.

Final Answer:
The statement that strain is directly proportional to stress within the elastic limit is known as Hookes law.