Question

The value of poisson's ratio lies between......... (A) - 1 to \((1 / 2)\) (B) \(-(3 / 4)\) to \([(-1) / 2]\) (C) \(-(1 / 2)\) to 1 (D) 1 to 2

Short answer

The value of Poisson's ratio lies between \(-1\) and \(\frac{1}{2}\).

Step-by-step solution

Recall the range of Poisson's ratio

Poisson's ratio, denoted by ν (nu), is a measure of how a material deforms under stress. Its values range from -1 to 0.5 for most materials. Simply put, Poisson's ratio is always between -1 and 0.5.

Compare the given options to the known range

Here are the given options: (A) - 1 to \((1 / 2)\) (B) \(-(3 / 4)\) to \([(-1) / 2]\) (C) \(-(1 / 2)\) to 1 (D) 1 to 2 Now, we simply need to determine which of these options fits within the known range of Poisson's ratio. (A) This option has the correct range, which is from -1 to 0.5. (B) The lower limit is correct, but the upper limit is incorrect. If this were the correct range, it would mean that Poisson's ratio could never be between -0.5 and 0.5, but we know from our understanding of the material property that this is not true. (C) The lower limit is incorrect, as Poisson's ratio can be between -1 and -0.5. The upper limit is also incorrect, as we know that the upper limit of Poisson's ratio is 0.5, not 1. (D) This range is entirely outside the known range of Poisson's ratio, so it is not the correct answer.

Choose the correct option

Comparing all given options to the known range of Poisson's ratio, we find that option (A) is the correct answer. The value of Poisson's ratio lies between -1 and \((1 / 2)\).

Key concepts

Material Deformation

Material deformation occurs when an external force or stress is applied to a material, causing it to change shape or size. This process is vital to understanding the mechanical properties of materials. When materials experience deformation, they may stretch, compress, twist, or bend. Each material responds differently based on its inherent properties.

• Elastic Deformation: Temporary change in shape or size, where the material returns to its original form once the stress is removed.
• Plastic Deformation: Permanent change in shape or size, where the material does not return to its original form even after the stress is removed.

Measuring how a material deforms helps engineers determine its suitability for various applications. By understanding deformation, we can predict how materials will behave under different conditions.

Stress

Stress is the force applied to a material, divided by the area over which the force is exerted. It's a crucial concept in the field of materials science and engineering. Stress can cause a material to deform, and it's important to understand how different materials react under stress.

• Tensile Stress: Occurs when forces act to stretch a material.
• Compressive Stress: Takes place when forces compress or push a material together.
• Shear Stress: Arises when forces are applied in parallel but opposite directions, causing the material to twist or shear.

Understanding stress is essential for designing structures and materials that can withstand different types of loads without failing.

Upper and Lower Limits

The concept of upper and lower limits is essential in understanding material properties like Poisson’s ratio. For Poisson’s ratio, the limits indicate the range in which values must fall to describe how materials deform.

• Upper Limit: The maximum value Poisson’s ratio can reach, which for most materials is 0.5. This represents the material’s ability to deform laterally to the same extent that it stretches axially.
• Lower Limit: The minimum potential value, usually -1 for many materials. This signifies a complete negative correlation between lateral and axial deformation, though such extreme values are rare.

Understanding these limits helps in selecting the correct materials for engineering needs, ensuring that the materials perform as expected under applied stresses.

Material Property

Material properties are the qualities that define how a material behaves under certain conditions. Poisson’s ratio is one such property, indicating how much a material will expand in directions perpendicular to a compressing or stretching force.

• Elastic Modulus: Defines the stiffness of a material. It complements Poisson’s ratio by giving insights into how much a material will deform under stress.
• Density: The mass per unit volume of a material, affecting its suitability for specific applications, especially where weight is a critical factor.
• Thermal Conductivity: Describes how well a material can conduct heat, crucial for applications in heat exchange or insulation.

Identifying the right material properties ensures that a material will perform its role effectively, making it a cornerstone in material selection for engineering and manufacturing.