Important MCQs on Mechanical Properties of Solids with Explanation

Ans. (C) Compressibility

Explanation: The fractional change in volume per unit increase in pressure is called compressibility. Compressibility is equal to strain by stress. Compressibility is the reciprocal of the bulk modulus. Compressibility is denoted by k. Compressibility is the proportion of how a given volume is diminished under tension.

Ans. (C) Shape

Explanation: Shearing stress changes the shape of the body. Shear stress in elastic solid or fluid is determined by the force per unit area that the various sections of the solid or fluid exert on one another in a direction parallel to their plane of contact. This stress is brought on by a shear that tends to cause the various sections or layers of the solid or fluid to move in different directions.

Ans. (D) 1

Explanation: Given two wires W1 and W2. The wires are composed of the same material and have the same length. 

Using,

\(\frac{F}{A}\)=Y \(\frac{\Delta l1}{l1} \)

\(\frac{F}{\pi r^2} \)=Y (4)⟶ for W1

For W2 ⟶

\(\frac{4\pi r^2Y}{4\pi r^2}\)=Y\(\frac{\Delta l_2}{l_2}\)

\(\frac{\Delta l_2}{l_2}\)=1

So, the strain of W₂ is 1.

Ans. (D) Elastic limit

Explanation: Hooke's law is the principle that states that the force needed to extend or compress a spring by some distance is proportional to that distance. This proportionality constant defines the Elastic limit. To predict plastic deformation, corrosion, and elastic deformation Hooke’s law is used. Hooke’s law formula is F=kx.

Ans. (C) Only solids

Explanation: Longitudinal strain is possible in the case of only solids. This happens because when force is applied only solids can have a length that can be stretched. Longitudinal strain is denoted by the epsilon symbol. The change in the length of the object to the original length of the object caused due to longitudinal stress is defined as the longitudinal strain.

Ans. (B) Invar steel

Explanation: The elasticity of a material is a physical property. It is defined as the capacity of material which returns to its original shape after applying stress. The elasticity of invar steel is independent of temperature. Where the elasticity of copper, brass, and silver is dependent on temperature. Elasticity and temperature are inversely proportional. If temperature increases then elasticity decreases. If temperature increases then elasticity decreases.

Ans. (C) Lateral strain 

Explanation: The ratio of the change in dimension at right angles to the applied force to the initial dimension is known as lateral strain. The lateral strain occurs perpendicularly in the objects when the load is applied.

Lateral strain= change in diameter/original diameter.

Ans. (B) There is a repulsive force between the molecules

Explanation:  When the intermolecular distance increases due to tensile force, then there will be a repulsive force between the molecules. The distance between two metals contained in the two molecules. The more tensile force increases intermolecular distance.

Ans. (B) decreases. 

Explanation: The Young’s modulus decreases when varying with the increase of temperature. Young’s modulus is used to know the stiffness of the material. Young’s modulus is the ratio of the tensile stress to the tensile strain. When the temperature is increasing the intermolecular binding decreases, strain is produced and Young’s modulus decreases. Young’s modulus is inversely proportional to temperature.

Ans. (B) Hydraulic pressure

Explanation: Internal restorative forces that are equivalent to and counter to the fluid's applied forces are created by the body. In this instance, the hydraulic stress, or internal restoring force per unit area, has a magnitude equal to the hydraulic pressure. The pressure applied by water on a structure or surface is known as hydraulic pressure. 

Hydraulic pressure is equal to F (force) / A (surface area)

Ans. (D) Elastomer

Explanation: Substances that can be stretched to cause large strains are called elastomers. An elastomer is a natural polymer that has elastic properties. The amount of deformation of a material when a force is applied is known as strain.

Ans. (C) \(\frac{1}{2}\) \(\frac{pgl^2}{Y}\)

Explanation: Let's take a rope with an area of A. now take a small section δy at distance Y. 

Stress due to this section= ρAg (δy/A)=ρdδy

The strain on section Y = \(\frac{\delta 1}{y}\)

Using stress and strain

Stress = Y *strain

⇨ ρgδy =Y* \(\frac{\delta 1}{y}\)

⇨∆1=\(\frac{p g}{y} \int_0^L y \delta y\)

⇨∆1=\(\frac{pgl^2}{2Y}\)