84 free MCQs on Mechanical Properties of Solids, each with its own worked answer and explanation. Stress, strain, Hookes law, and the elastic moduli that describe how solids deform and recover under load.
Take the timed Mechanical Properties of Solids chapterwise test →84 practice questions on Mechanical Properties of Solids, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Mechanical Properties of Solids notes.
A typical stress-strain curve: the initial straight line (Hooke's Law region, slope = Young's modulus) ends at the elastic limit; beyond the yield point, deformation becomes permanent, peaking at the ultimate tensile strength before the wire finally fractures.
Q1.
The ratio of shear stress to shear strain is called the:
Q2.
When a wire is stretched longitudinally within the elastic limit, its diameter:
Q3.
The negative sign in the definition of bulk modulus indicates that:
Q4.
A gas possesses only:
Q5.
Which of the following is a dimensionless quantity?
Q7.
Strain is defined as the ratio of:
Q8.
Which type of stress changes only the shape of a body, not its volume?
Q9.
Hookes law states that within the elastic limit:
Q10.
Youngs modulus is defined for which type of deformation?
Q11.
The bulk modulus relates pressure change to:
Q12.
Which material would have the smallest bulk modulus?
Q13.
Poissons ratio is the ratio of:
Q14.
On a stress-strain curve, the point beyond which the material does not return to its original shape after removing load is called the:
Q15.
The SI unit of the modulus of elasticity (Y, G, or B) is the same as that of:
Q16.
Which of these materials is the most ductile (shows large plastic deformation before fracture)?
Q17.
Elastic potential energy stored per unit volume of a stretched wire is given by:
Q18.
Which of the following best describes a perfectly plastic material beyond its yield point?
Q19.
The property by which a body regains its original shape after the deforming force is removed is:
Q20.
Stress is defined as the deforming force acting per unit:
Q21.
Strain is the ratio of the change in a dimension to its:
Q23.
Strain is a quantity that has:
Q24.
A material that keeps its new shape after the deforming force is removed is described as:
Q25.
Within the elastic limit, stress is directly proportional to strain. This statement is:
Q26.
A wire of length 1 m and cross-section 2 mm<sup>2</sup> stretches by 0.5 mm under a load of 200 N. Its Young's modulus is:
Q27.
A wire of radius 1 mm carries a tension of 31.4 N. The tensile stress in the wire is:
Q28.
A wire elongates by 2 mm under a load. A second wire of the same material and length but half the radius, under the same load, elongates by:
Q29.
A wire under a stress of 10<sup>8</sup> Pa has a strain of 10<sup>-3</sup>. The elastic energy stored per unit volume is:
Q30.
A wire of length 2 m and cross-sectional area 1 mm² is stretched by 1 mm under a load of 100 N. What is its Youngs modulus?
Q31.
Two wires of the same material have radii in ratio 2:1 and lengths in ratio 1:2. If stretched by the same force, the ratio of their elongations (ΔL<sub>1</sub>:ΔL<sub>2</sub>) is:
Q32.
A solid sphere of volume V is submerged in a fluid such that pressure increases by ΔP, causing a volume decrease ΔV. If bulk modulus is B, which expression is correct?
Q33.
A metal cube of side 10 cm is subjected to a shearing force on its top face, causing a lateral displacement of 0.05 cm. What is the shearing strain?
Q34.
Two springs of force constants k1 and k2 connected in series behave like a single spring of effective Youngs-modulus analog with stiffness k. Which formula gives k?
Q35.
A wire stretches by 1 mm under a certain load. Another wire of the same material, but with double the length and double the diameter, stretches under the same load by:
Q36.
If the Poissons ratio of a material is 0.5, the material is best described as:
Q37.
A rubber cord has a cross-sectional area 1 mm² and total unstretched length 10 cm. It is stretched to 12 cm. If Youngs modulus of rubber is 5 × 10⁸ Pa, the tension in the cord is:
Q38.
For a given material, which modulus generally has the largest numerical value?
Q39.
A beam supported at both ends sags under its own weight. To minimize the sag (depression) without significantly increasing material used, engineers use a beam with cross-section shaped like:
Q40.
A wire is stretched within its elastic limit and then the load is removed. The wire returns to its original length. This behaviour is called:
Q41.
If a material has Youngs modulus Y and shear modulus G with G < Y always, this physically implies that compared to stretching, a given material:
Q42.
Young’s modulus is the ratio of tensile (longitudinal) stress to:
Q43.
The bulk modulus of a material relates stress to a change in:
Q44.
The modulus of rigidity is associated with ___ strain:
Q45.
The reciprocal of the bulk modulus of a material is called its:
Q46.
Steel is more elastic than rubber because steel has a ___ Young’s modulus:
Q47.
The stress beyond which a material begins to deform permanently is called the:
Q48.
The dimensional formula of stress is the same as that of:
Q49.
For a stretched wire within the elastic limit, the ratio of stress to strain gives the:
Q50.
A steel wire of Young modulus 2 × 10<sup>11</sup> Pa is stretched by 0.1% of its original length. The tensile stress developed in the wire is:
Q51.
A wire of cross-section 1 mm<sup>2</sup> and Young's modulus 2×10<sup>11</sup> Pa is stretched to a longitudinal strain of 0.05%. The force applied is:
Q52.
A rod (Y = 2×10<sup>11</sup> Pa, α = 1.2×10<sup>-5</sup> /K) is clamped rigidly between two walls and heated through 50 K. The thermal stress developed is:
Q53.
A wire of given material and radius can support a maximum load W before breaking. A wire of the same material and radius but twice the length can support a maximum load of:
Q54.
A steel wire (Y = 2×10<sup>11</sup> Pa) and a copper wire (Y = 1×10<sup>11</sup> Pa) of equal length and cross-section are joined end to end and stretched by the same force. The ratio of their elongations (steel : copper) is:
Q55.
A metal cube of side 0.1 m has a tangential force of 100 N applied to its top face. If the shear modulus is 2.5×10<sup>10</sup> Pa, the lateral displacement of the top face is:
Q56.
A uniform wire of length L and cross-section A hangs vertically under its own weight (density ρ). The total elongation due to its own weight is:
Q57.
Two wires A and B of the same material and same length, but radius of A is twice that of B, are stretched by the same force. The ratio of elastic potential energy stored in A to that in B is:
Q58.
A composite rod is made of two equal-length segments, one of Youngs modulus Y1 and area A, and the other of Youngs modulus Y2 and the same area A, joined end to end and stretched by force F. The effective Youngs modulus of the composite rod is:
Q59.
A spherical ball of volume V made of a material with bulk modulus B is dropped into a lake to depth h. The fractional decrease in volume (ΔV/V) at that depth (ignoring atmospheric pressure) is approximately:
Q60.
A metal wire of Youngs modulus Y is stretched by a load such that the strain is x. If the load is increased so the strain doubles (still within elastic limit), how does the elastic energy stored per unit volume change?
Q61.
A rod fixed between two rigid walls is heated so that it would expand by ΔL if free, but the walls prevent any expansion. If Youngs modulus is Y, area A, and coefficient of linear expansion is α, the thermal stress (compressive force per area) developed is:
Q62.
In a tensile test, a metal sample shows necking (localized thinning) just before fracture. This occurs at a stress level called the:
Q63.
A wire is replaced by another wire of the same material but with half the diameter, used to support the same load, suspended for the same length. Compared to the original, the new wire is:
Q64.
Steel is preferred over copper for the same length and load-bearing cable application primarily because, for steel:
Q65.
A cube of side a is subjected to three mutually perpendicular equal stresses sigma on its faces (hydrostatic compression). If Youngs modulus is Y and Poissons ratio is sigma_p, the fractional decrease in volume in terms of bulk modulus B is given by ΔV/V = 3σ/Y multiplied by a factor. That factor, expressed using Poissons ratio, is:
Q66.
From Y = F·L/(A·ΔL), doubling the length of a wire (other factors fixed) makes the extension:
Q67.
Poisson’s ratio is the ratio of lateral strain to:
Q68.
The elastic potential energy stored per unit volume in a stretched wire equals:
Q69.
A material that can be drawn out into thin wires is said to be:
Q70.
The area under a stress–strain curve represents the ___ stored per unit volume:
Q71.
Two wires of the same material, one twice as thick as the other, carry the same load. The thicker wire extends:
Q72.
The breaking stress of a material depends on the:
Q73.
Within the proportional limit, the graph of stress against strain is a:
Q74.
The three elastic moduli are Young’s modulus, bulk modulus and the:
Q75.
A perfectly rigid body would have a Young’s modulus of:
Q76.
Elastic hysteresis refers to the lag of strain behind stress during loading and unloading, seen most clearly in:
Q77.
A weight stretches a wire by 1 mm. A second wire of the same material but double the length and double the radius carries the same weight. Its elongation is:
Q78.
A rod is rigidly clamped between two fixed walls and its temperature is raised by ΔT. The thermal stress developed (Y = Young modulus, α = expansion coefficient) is:
Q79.
The elastic energy stored per unit volume of a stretched wire, in terms of stress σ and Young modulus Y, is:
Q80.
A wire is stretched so that its longitudinal strain is 0.1%. If Poisson ratio is 0.3, the magnitude of the lateral (radial) strain is:
Q81.
A pressure of 10⁷ Pa is applied to a material of bulk modulus 2×10⁹ Pa. The fractional change in its volume is:
Q82.
The breaking force of a wire is proportional to its cross-sectional area. If the radius of a wire is doubled, its breaking force becomes:
Q83.
A force of 100 N stretches a wire by 2 mm. The work done in stretching it is:
Q84.
A steel wire (Y = 2×10¹¹ Pa) carries a stress of 2×10⁸ Pa. The percentage longitudinal strain is:
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