Mechanical Properties of Solids Mock Test – Class 11 Physics

1. A wire has length and cross-sectional area . A point on its load-extension graph corresponds to load and extension . The corresponding point on its stress-strain graph has coordinates

2. A short record of observations is given below.

Which classification is most suitable?

3. The table gives possible design changes for a cable carrying the same load.

The suitable matching is

4. A lift of mass is pulled upward with acceleration by a steel cable of length . Take , , breaking stress , and required factor of safety . If the cable extension must not exceed , the minimum cross-sectional area required is

5. A tangential force acts on the top face of a solid block of area , while the lower face is fixed. If the upper face shifts sideways by and the height of the block is , the shear modulus is

6. A block of height and top-face area is sheared by a tangential force. Its shear modulus is . If the elastic energy stored in shear is given by , what force is needed to store ?

7. 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

8. Assertion : A rubber band can return nearly to its original length after unloading even when its stress-strain curve is non-linear.
Reason : Elastic recovery and exact proportionality between stress and strain are the same condition.

9. A wire is stretched in the linear elastic range. Its stress is increased from to , while the material remains the same. The elastic energy density becomes

10. A material reaches its elastic limit at stress , yields at stress , and breaks at stress . A working stress chosen below is mainly intended to ensure

11. A shear test gives the following data for three identical blocks.

The shear moduli are

12. A block is glued to a rigid table, and a horizontal force is applied to its top surface. A second identical block is not glued and simply slides when the same force is applied. The first setup is better for studying shear modulus because

13. 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

14. A tensile stress-strain curve for a ductile metal rises after yielding before reaching its maximum stress. This rise after yielding is most closely associated with

15. A material shows a long nearly horizontal region on its stress-strain curve after the elastic part, and it can be drawn into a wire before fracture. This combination most strongly indicates

16. A rope of cross-sectional area is used to lift a load of . If its breaking stress is , the factor of safety during this lift is

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

18. Consider the following statements about bulk modulus.
I. It relates pressure change to volumetric strain.
II. Its SI unit is .
III. A larger value usually means the material is less compressible.
IV. It is dimensionless because volumetric strain is dimensionless.
The suitable set is

19. Use the testing notes below.

The correct matching is

20. 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

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

22. Assertion : The breaking load of a uniform wire depends on its cross-sectional area.
Reason : For a given material, breaking load is .

23. Two wires are joined end-to-end and stretched by the same tensile force . Wire has , , and . Wire has , , and . The total extension and elastic energy stored in the combination are

24. The following table lists common loading situations.

The most suitable stress names for , , and are

25. Assertion : A solid with a large shear modulus undergoes a small angular deformation under a given shearing stress.
Reason : Shearing strain is equal to shearing stress divided by shear modulus in the linear elastic range.

26. 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

27. A pressure sensor contains a small solid part that must undergo very little volume change even under large pressure. The material should preferably have

28. 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

29. A liquid-like pressure is applied equally on all faces of a small solid cube. The cube’s volume decreases slightly but its shape remains almost similar. This situation is the most suitable setup for measuring

30. A wire is stretched to a longitudinal strain of . Its Poisson’s ratio is . Using the small-strain estimate , the approximate volume strain is

31. A cylindrical wire is stretched, and its diameter decreases. If the diameter is used to find lateral strain, the correct expression and sign for stretching are

32. In a graph-based elastic test, the slope of the stress-strain graph is . A wire of the same material has and . The slope of its load-extension graph is

33. 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

34. A beam bends downward under a central load. The top surface is compressed, the bottom surface is stretched, and a neutral layer lies between them. This description shows that bending mainly involves

35. 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

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

37. 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

38. A steel rod with and is heated by while its expansion is completely prevented. Using , the thermal stress is

39. A block of height has its upper face displaced sideways by under a tangential force. The shearing strain is

40. The data below refer to normal forces acting on different flat faces.

The stresses in , , and are in the ratio

41. A metal strip is stretched up to a point beyond its elastic limit and then unloaded. Its final length is slightly greater than its original length. This leftover extension is called

42. The following claims are made after a full elastic test of a wire.
I. The slope of the stress-strain graph gives Young’s modulus.
II. The area under the force-extension graph gives work done.
III. The area under the stress-strain graph gives elastic energy density.
IV. The slope of the force-extension graph is always equal to Young’s modulus.
The suitable set is

43. A metal rod is fixed at both ends. It is first heated by and later cooled by from its original temperature. If expansion or contraction is completely prevented in both cases, the nature of the thermal stress is

44. When a spring is stretched slightly and held at rest, an internal force develops in the spring. This internal force mainly acts to

45. A load-extension graph for a wire is a straight line with slope . The wire has length and cross-sectional area . Young’s modulus of the wire material is

46. A cube made of a material with larger shear modulus is compared with an identical cube made of a material with smaller shear modulus. Under the same tangential stress, the larger- cube shows

47. A solid sphere of volume is taken deep underwater where the pressure increase is . Its bulk modulus is . If the material also has and is isotropic, use to find the volume decrease and Young’s modulus.

48. 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

49. 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

50. Match each graph description with its correct physical meaning.

The correct matching is