Mechanical Properties of Solids Mock Test – Class 11 Physics

1. Consider the following statements about working stress and material failure.
I. Working stress should be lower than breaking stress.
II. Factor of safety is .
III. A factor of safety greater than means the material is used below its breaking stress.
IV. Working stress is the same as breaking stress in safe design.
The suitable set is

2. A material has Young’s modulus and is stretched to a strain of within the elastic limit. The elastic energy density is

3. A wire of radius , length , and Young’s modulus is stretched by force . A second wire of the same material is to have the same extension under the same force but has length . Its radius should be

4. A spring returns to its original length after a small load is removed, but it remains slightly longer after a much larger load is removed. This observation mainly shows that

5. A final material-choice note says: “Choose the cable with largest , largest breaking stress, and adequate area.” This recommendation is physically sensible because it tries to obtain

6. A load-extension graph for a rubber band during loading lies above the unloading curve for the same extension. For one complete cycle, the energy lost is represented by

7. A force of acts normally on an area of . The stress produced is

8. A wire has a straight load-extension graph. At , its extension is . Its load-extension slope is

9. An -shaped steel girder is often used in bridges and buildings because much of its material is placed far from the neutral layer. The main benefit is that it

10. A student reads a stress-strain graph and says, “The area under the graph is Young’s modulus.” The best correction is that the area under a stress-strain graph gives

11. A circular cable is designed using the stress formula . A learner uses the diameter directly in . The corrected area expression should be

12. A wire is under stress . Material has , while material has . If both wires have the same original length, the ratio of their strains is

13. Consider the statements below.
I. A high helps reduce extension under a given tensile stress.
II. A high helps reduce fractional volume change under pressure.
III. A high helps reduce shearing strain under a given shearing stress.
IV. A high compressibility means the material strongly resists volume change.
The suitable set is

14. A material is loaded only within the initial straight part of its stress-strain graph and then unloaded. The most likely observation is that the material

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

16. Two wires of equal length are fixed in parallel between the same supports and share a load. Wire has , , and breaking stress . Wire has , , and breaking stress . If the factor of safety is for both wires and the common extension must not exceed , the maximum total load is

17. For many ordinary comparisons, gases are more compressible than liquids and solids. In terms of bulk modulus, this means gases usually have

18. A straight force-extension graph is drawn for a wire. A straight stress-strain graph is also drawn for the same wire and the same loading range. If the force-extension graph area is multiplied by , the result is

19. A student says that stress, elastic energy density, and Young’s modulus are the same quantity because all can be expressed in . The best correction is that

20. Assertion : In the initial straight part of a stress-strain graph, the slope gives the elastic modulus.
Reason : The slope is , and stress is proportional to strain there.

21. In a material test, the following observations are made: the first part of the stress-strain graph is straight; after that the curve bends; still later, unloading leaves permanent strain. The sequence of ideas represented is

22. A lift cable must satisfy two conditions: the working stress must not exceed , and its extension under a load must remain small. If the load and cable length are fixed, increasing the cross-sectional area mainly

23. A wire is stretched slowly from zero load to a final load , producing final extension . The work done in stretching the wire is not but because

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

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

26. A lift of mass is moving upward but slowing down with acceleration downward. It is supported by a cable of length , area , and . Take and cable breaking stress . The extension and factor of safety at that instant are

27. Consider the statements about a tensile stress-strain curve.
I. The proportionality limit marks the end of strict stress-strain proportionality.
II. The elastic limit is connected with complete recovery on unloading.
III. Ultimate tensile strength is the maximum stress reached on the curve.
IV. Breaking point must always occur at the maximum stress point.
The suitable set is

28. A wire carrying a suspended load is held at rest after a small extension. At that instant, the internal restoring force in the wire is best described as

29. A solid cube is compressed uniformly by pressure and also tested under tangential shear in a separate setup. Under the same pressure increase, material has a smaller fractional volume change than material . Under the same shearing stress, has a smaller shearing strain than . The best comparison is

30. A wire of length , cross-sectional area , and extension is pulled by a force within its elastic limit. The expression for Young’s modulus is

31. A long thin pillar and a short thick pillar are made of the same material and have the same cross-sectional area at the base. Under large compressive loads, the long thin pillar is more likely to fail by sideways bending. This qualitative failure is called

32. A passage describes a testing setup: a wire is first loaded within the straight part of its force-extension graph, then loaded beyond the elastic limit, and finally unloaded. The observation most consistent with this description is

33. A material-testing report says that sample has high stiffness and breaks after a very small plastic region, while sample has lower stiffness but can undergo a long plastic stretch before fracture. The safer interpretation is that

34. A beam is bent downward by a load at its middle. A designer increases the depth of the beam while keeping much of the material near the top and bottom faces. The main reason this improves resistance to bending is that

35. 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

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

37. A rectangular eraser is pushed sideways on its top face while its bottom face is held fixed. The top face shifts slightly, but the volume changes very little. The deformation is best described as

38. A cable of area carries a load of . Its breaking stress is . The factor of safety is

39. 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

40. A solid block of height and top-face area is sheared by a tangential force . If the material has shear modulus , the sideways displacement of the top face is

41. A final check of an elastic calculation gives , , and energy density . These values are consistent with the linear elastic relation because

42. In a stretched wire at rest, the stress is often calculated using the external load . Strictly, stress in the wire is related to

43. Assertion : , , and all have the unit .
Reason : Each of them is a ratio of an appropriate stress to an appropriate strain.

44. A cable must carry . Its length is , , breaking stress is , and the factor of safety is . If the extension must not exceed , the minimum cross-sectional area required is

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

46. A passage describes a cable test: the load is increased slowly, the extension is recorded, and the graph remains straight up to . At , the extension is . If the cable volume is , the elastic energy density at this point is

47. A square concrete pillar of side supports a load of . The average compressive stress in the pillar is

48. In a stress-strain graph, Region is a straight line through the origin, Region is a curved but still recoverable part, Region leaves permanent strain after unloading, and Point is the highest stress reached. The best interpretation is

49. A material is stretched in its linear elastic region. If the stress is and Young’s modulus is , the elastic energy density can also be written as

50. A lift of mass is supported by a cable of area . Taking , the working stress in the cable while the lift is at rest is