Mechanical Properties of Solids Mock Test – Class 11 Physics

1. An isotropic elastic solid has and . Using and , its and are respectively

2. A block of area and height is acted on by a tangential force of . If , the sideways displacement of its upper face is

3. In SI units, stress is measured in ______.

4. A learner compares two wires under the same load and says, “The thicker wire stretches less only because it has less stress.” The most complete correction is that the thicker wire stretches less because

5. A stress-strain graph has stress on the vertical axis and strain on the horizontal axis. In the linear region, a point has coordinates , . A wire of this material has and . The corresponding load and extension are

6. The elastic-constant relations , , and should be applied carefully because

7. A wire is replaced by another wire of the same material and length, but with twice the diameter. Under the same load and within the elastic limit, the extension becomes

8. A rod of length is heated by . Case : it is free to expand. Case : it is completely prevented from expanding. The most accurate comparison is

9. The dimensional formula of elastic modulus is the same as that of

10. The same material is made into two wires of equal area but different lengths. Their stress-strain graphs in the elastic region will have the same slope, while their load-extension graphs may have different slopes. The reason is that

11. Consider the statements below about the elastic modulus.
I. It is the ratio of stress to strain in the elastic region.
II. It has the same SI unit as stress.
III. A larger modulus generally means smaller strain for the same stress.
IV. It is always dimensionless because strain is dimensionless.
The correct set is

12. A lift cable is rated with a factor of safety . This means the working stress is

13. A cable must carry safely with factor of safety . If the material breaking stress is , the minimum area required is

14. A material sample is tested in tension. At a certain point, , , and the sample volume is . Assuming linear elastic behaviour up to this point, the elastic energy stored in the sample is

15. A shear stress-shear strain graph for a material is a straight line through the origin. At shearing strain , the shearing stress is . The slope of the graph is

16. A material’s stress-strain graph in the elastic range is converted into a force-extension graph for a particular wire made from that material. If the wire length is doubled while the area remains unchanged, the force-extension slope becomes

17. Mechanical properties of solids mainly describe how a solid behaves when an external force tries to deform it. What is the most suitable description of this idea?

18. A rubber band is stretched gently and then released. It almost returns to its original length. This behaviour is best described as

19. The SI unit of shear modulus is

20. A steel bar with and is heated by . If only of its free expansion is prevented, the thermal stress is

21. A material is tested under the same tensile stress and the same pressure increase in two separate experiments. It shows small tensile strain but large fractional volume change. The best description is that the material has

22. A metal wire and a putty strip are both permanently deformed after loading. The metal wire showed elastic behaviour at small loads before yielding, while the putty retained shape even after gentle pressing. The better comparison is that

23. A wire is stretched slowly and then unloaded along a different path on the force-extension graph. The loading area is , and the unloading area is . The energy lost in one cycle is

24. A student compares two stress-strain graphs in their initial linear regions. Graph is steeper than graph . For the same small strain, graph must have

25. A metal wire is stretched beyond the range in which it can fully recover. After unloading, its final length is larger than its original length. The extra length left behind is an example of

26. Compressibility is related to bulk modulus by

27. A uniform wire of volume is stretched in the linear elastic region. Its elastic energy density is , and . The stress and total elastic energy are

28. A material has a very large Young’s modulus but a low breaking stress. For a long suspension cable, this means the material may

29. A suspension cable is replaced by another cable of the same material and length but with radius increased by . Under the same working load, the new cable’s extension becomes

30. Consider the statements below.
I. Stress and elastic moduli have the same dimensional formula.
II. Strain and Poisson’s ratio are dimensionless.
III. Elastic energy density has the same dimensional formula as stress.
IV. Compressibility has the same unit as bulk modulus.
The suitable set is

31. A student writes without the negative sign. The main problem with this notation for an ordinary stretched wire is that it would make

32. A rod of length , area , , and is heated by . Its expansion is completely prevented. The compressive force in the rod and the elastic energy stored are

33. A stress-strain graph for an elastomer is non-linear, but after unloading from a large strain the sample nearly regains its original length. The property shown is best described as

34. A thin metal ruler is held at one end and gently bent at the other end. In this situation, the word deformation refers to the ruler's change in

35. A student claims that has unit because volume appears in the formula. The correct unit is because

36. A table compares three materials under the same pressure increase.

The material with largest bulk modulus and the material with largest shear modulus are respectively

37. A rod is heated while it is completely prevented from expanding. A student wants to use the free expansion formula only and conclude that no stress is produced because the length does not change. The missing idea is that

38. A material is reported to have and . If the material is isotropic, its Poisson’s ratio is

39. The following table lists three design needs.

The suitable matching is

40. A stress-strain curve for a metal is linear at first, then gradually bends away from the straight line while the material still returns to its original length on unloading. The bending away first indicates that

41. An isotropic material has and . Using and , its Young’s modulus and Poisson’s ratio are closest to

42. A solid sphere of volume is taken to a region where pressure increases by . If , the decrease in volume is

43. A solid of volume is compressed by pressure so that its volume changes by . The ratio in the bulk modulus formula represents

44. A block is pressed uniformly from all sides so that its shape remains almost the same but its volume decreases slightly. This is mainly a case of

45. Consider the statements below about common calculation errors.
I. Using load instead of stress can hide the effect of cross-sectional area.
II. Using extension instead of strain can hide the effect of original length.
III. Using instead of overestimates circular area.
IV. Using area under a stress-strain graph as modulus is correct in the linear region.
The suitable set is

46. For an isotropic material, and . Using , the shear modulus is

47. The dimensional formula of stress is

48. A wire of length is stretched so that its length increases by . What is its longitudinal strain?

49. The SI unit and dimensional formula of bulk modulus are respectively

50. A wire has stress and strain at a certain point in the linear elastic region. Its volume is . If the stress is increased to without leaving the linear region, the new total elastic energy stored is