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Mechanical Properties of Solids

8 Marks Question:
1) Define Hooke's law of elasticity? Describe Searle's method to determine the
Young's modules of the material of a wire.
 Ans: Hooke's law:
  "With in the elastic limit, stress is directly proportional to the strain".
   Stress  strain
   Stress = E × strain

  Where E = modulus of Elasticity
Experimental determination of Young's modules of a wire:
i) The apparatus consists of two identical wires W1 and W2 made of same material, W1 is called reference wire and W2 is called experimental wire.     

ii) These two wires are suspended from A ceiling as shown in figure.
iii) Two frames A and B are Suspended from the ends of the wires with the help of chuck nuts
iv) The two frames are arranged parallel with help of horizontal links (D1, D2)
v) A micrometer is placed in the frame B. A spirit level is placed horizontally from
frame 'A' to frame B, so that its free end rests on micrometer.
vi) A dead weight is attached to frame A. A load pan is attached to frame B.
The initial length of the wire (l) and radius (r) of wire are measured.
i) When the load in the pan is increased then wire W2 is elongated. Hence B is lowered, the spirit level shows un level.
ii) Adjust the micrometer such that the air bubble in the spirit level comes to centre. Note the reading of micrometer.
iii) Remove the load on the pan and frame B goes to its original position. Adjust the micrometer until spirit level shows initial level Note the reading of micrometer.
iv) The same procedure is repeated with different loads and readings of micrometer while loading and unloading. Values are tabulated as follows.

4 Marks Question:
2) Describe the behaviour of a wire under gradually increasing load.
Ans: Let us consider a wire clamped at one end and a load is applied at the other end. the load is gradually increased from zero to the value until the wire breaks down.
    Draw the stress-strain curve by taking strain on X- axis and stress on Y- axis. On the graph points A, B, C, D, E are located.

Proportionality limit (A).
    The maximum stress applied on the wire up to which stress is directly proportional to strain and Hooke's law is obeyed is called proportionality limit. OA is a straight line. At this stage when      
stress is removed the wire regains its original shape and size.
Elastic limit (B)
    If stress is further increased from A, the wire does not obey Hooke's law up to point B. But still elastic nature of the wire exist. Hence maximum stress up to which strain produced without effecting the elastic nature of the wire is called elastic limit. Points A and B are very nearer and may coincide for some materials.
Permanent Set:
If the wire is loaded beyond elastic limit B. The wire gets stretched permanently. oo' is called permanent set.
Yield point: (C)
    If wire is further loaded beyond 'C' the extension of the wire increases rapidly without any increase in the load. The stress for which, the extension of a wire begins to increase with out any further load is called yield point or yield stress.
Breaking stress:
    At point 'D' the wire begin to thin down and at point 'E', it breaks. At point D the value of stress developed is maximum and is called ultimate tensile strength. The stress corresponding to point C
is called breaking stress. Beyond the point D, the Diameter of wire decreases even without increase in load and breaks at E.
2 Marks Questions
3) "Steel exhibits more elastic nature than rubber" explain.
Ans: Two identical rods, one is made of rubber and second one is made of steel are
taken. Let both are pulled by same force, their expansions are eR, eS and young modulii
are YR, YS respectively. we know Y  1/e. Here eR > eS hence YR < YS. Hence
steel is more elastic than rubber.
2. Define Hooke's law of elasticity?
    Ans: Within the proportionality limit, the applied stress on a body is directly proportional
to the strain produced in it.
   i.e., stress  strain
   Stress = E × strain
   E = stress / strain          Where E is called modulus of Elasticity.

4) State the theoretical limits of poisson ratio.
    Ans: Theoretical limits of Poisson ratio are - 1 to +0.5
5) State the practical limits of poisson ratio?
     Ans: practical limits of Poisson's ratio are 0 to 0.5.

Posted Date : 02-11-2020

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.

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