Question

Assertion and Reason: Read the assertion and reason carefully to mark the correct option out of the option given below (A) If both assertion and reason are true and reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not the correct explanation of the assertion. (C) If assertion is true but reason is false. (D) If assertion and reason both are false. Assertion: The stretching of a coil is determined by its shear modulus. Reason: Shear modulus change only shape of a body keeping its dimensions unchanged. (A) a (B) $\mathrm{b}$ (C) $\mathrm{c}$ (D) $\mathrm{d}$

Short answer

C

Step-by-step solution

Evaluate the assertion

The assertion states that the stretching of a coil is determined by its shear modulus. This is true as the shear modulus determines how much a material can resist shearing forces which in turn helps us to determine the stretching of a coil. Therefore, the assertion is true.

Evaluate the reason

The reason states that the shear modulus change only shape of a body keeping its dimensions unchanged. This is not true. The shear modulus is a measure of a material's ability to resist shearing forces and it might lead to changes in the dimensions of a body depending on the magnitude of the force acting on the body. Therefore, the reason is false.

Compare the assertion and reason

Since the assertion is true and the reason is false, the correct answer is option C. This means that the assertion is true, but the reason is false and doesn't provide the correct explanation of the assertion. Answer: $C$.

Key concepts

Material Science

Material Science is a field that focuses on understanding the properties and behaviors of materials. This knowledge helps in exploring new ways to improve, manipulate, and use materials across various industries. Understanding how materials respond to different kinds of forces, such as shearing or stretching, allows scientists and engineers to create products that are durable and efficient. For example, knowing a material's shear modulus will assist in determining how materials can be used in applications requiring resistance to shearing forces.
Material scientists aim to:

• Discover new materials with superior properties.
• Enhance existing materials for better performance.
• Ensure materials are cost-effective and sustainable.

This discipline covers a range of materials from metals and ceramics to polymers and composites. Each type has distinct characteristics that influence its application.

Stress and Strain

Stress and strain are fundamental concepts in the study of materials that explain how materials deform under various forces. Stress refers to the force applied to a material divided by the area over which the force is applied. It describes the intensity of the internal forces within a material. Strain, on the other hand, is the measure of the deformation of the material as a response to the stress applied. It is a dimensionless number, describing how much the material has lengthened or shortened compared to its original length.
Understanding the relationship between stress and strain helps in assessing the performance and stability of materials under mechanical forces.

• Stress: Measured in units like Pascals (Pa). Calculated as force over area ($\sigma =\frac{F}{A}$).
• Strain: A ratio with no units, calculated as the change in length over original length ($ϵ=\frac{\mathrm{\Delta }L}{L_0}$).

These measurements are key for determining materials' limits and their subsequent applications in real world scenarios.

Elasticity

Elasticity is a property that describes a material's ability to return to its original shape after being deformed by an external force. When a material exhibits high elasticity, it can withstand significant forces without permanent deformation. Understanding elasticity is crucial in design and engineering because it ensures that structures and materials can handle stresses and strains over time without failure.
Key features of elasticity include:

• Elastic Limit: The maximum amount of stress a material can withstand while still being able to return to its original shape after the stress is removed.
• Hooke's Law: Defines the relationship between stress and strain in the elastic region of a material, expressed as $\sigma =E\cdot ϵ$, where $E$ is the Elastic Modulus.
• Elastic Modulus: A measure of a material's stiffness. The higher the modulus, the stiffer the material.

In practical terms, designing with elasticity in mind helps prevent material fatigue and failure, ensuring longevity and reliability of products.