Mechanical Properties of Solids Important Questions

Ans: Pressure is taken as positive when it compresses the material, but volume decreases. The negative sign ensures that the bulk modulus is positive.

Ans: Yes, in some auxetic materials (e.g., certain foams), Poisson's ratio is negative – they expand laterally when stretched.

Ans: Diamond has the highest Young's modulus (≈ 1200 GPa) among known materials.

Ans: Poisson’s ratio depends on molecular structure and lateral contraction behaviour, whereas Young’s modulus depends on bond strength. Rubber has weak intermolecular forces (low Young's modulus, Y) but a similar lateral response to steel.

Ans: Generally, elastic moduli decrease with a rise in temperature because thermal vibrations weaken interatomic forces.

Ans: Yes, strain is a second-rank tensor because it has both normal and shear components in three dimensions.

Ans. It is defined to be the ratio of change in length to the original length of an object when it gets deformed by an external force, i.e. Longitudinal strain = l /L= change in length/ original length

Ans. It is defined as the ratio of change in volume per unit of the original volume of the body when deformed by an external force change in volume AV i.e. Volumetric strain = change in volume/ original volume =ΔV/V

Ans. It is defined as the restoring force developed per unit area of cross-section of a body when the length of the body increases in the direction of the deforming force.

Read More: Stress

Ans. Three states of matter differ from each other due to the following two factors:

(a) The different amounts of tester atomic and intermolecular forces.

(b) The degree of haphazard thermal motion of the atoms and molecules of a substance depends upon the temperature.

Ans. In a normal situation/circumstances, the atoms of a solid are at the locations of minimum potential energy. When we intentionally stretch a wire, the work has to be done against interatomic forces. This work is stored in the wire in the form of elastic potential energy for the time being.

Ans. (a) The following factors affect the elasticity of a material:

• Effect of hammering and rolling on a material: It causes a decrease in the plasticity of the material due to the break-up of crystal grains into smaller units and thus, the elasticity of the material increases.
• Effect of Annealing on a material: Annealing results in an increase in the plasticity of the material due to, the formation of large crystal grains. Henceforth, the elasticity of the material decreases.
• Effect of the presence of impurities on a material: The effect of the presence of impurities in a material can be both ways i.e. it can increase as well as decrease the elasticity of the material. The type of effect depends upon the nature of the impurity present in the material.
• Effect of temperature on a material: In most cases, an increase in the temperature of the material causes a decrease in the elasticity of the material. The elasticity remains constant with temperature.

(b) Poisson’s Ratio (σ): Within elastic limits, it is defined as the ratio of lateral strain (β) to the linear strain, i.e. σ = βα

(c) Breaking Load: It is defined as the product of the breaking stress and area of cross-section of the given object. It is also called the maximum load a body (cable/ wire) can support or hold i.e. it is given as breaking load = Breaking stress × area of cross-section. It should be noted that breaking stress is always constant for the given material.

Ans. A bridge, during its use, undertakes alternative strains a large number of times each day, depending upon the movement of vehicles on it. When a bridge is used for a long time, it exhausts its elastic strength, resulting in a significant increase in the number of strains in the bridge for a given stress. Ultimately, the bridge may collapse. Thus, to avoid this, the bridges are stated to be unsafe after long use.

Ans. Spring should have a large restoring force, which is set up in it when it is deformed, which in turn depends upon the elasticity of the material of the spring. Since Young’s modulus of elasticity of steel is more than that of copper, steel is preferred in making such springs.

Read More: Interaction of Forces & Effects of Force Interaction

Answer: a) Pascal

Stress = Force/Area = N/m2 = Pascal.

2. Within the elastic limit, the stress is proportional to strain. This was stated by:

1. Newton
2. Hooke
3. Young
4. Poisson

Answer: b) Hooke

3. Toisson’s ratio cannot have a value:

1. 0.1
2. 0.5
3. 0.8
4. -o.1

Answer: c) 0.8

For isotropic materials, −1 < ν < 0.5. Value > 0.5 violates

Thermodynamic stability.

4. Energy stored in a stretched wire of length L, across-section A, stretched by ΔL is:

1. (Y A (ΔL)²)/(2L)
2. (Y A ΔL)/(2L)
3. (Y A (ΔL)²)/L
4. Y A ΔL / L

Answer: a) (Y A (ΔL)²)/(2L)

U = (½) x stress x strain x volume = (½) x (Y strain) x strain x

(AL) = (Y A (ΔL)²)/(2L)