JEE Main & Advanced Physics Elasticity Question Bank

done Critical Thinking Total Questions - 8

• question_answer1)
  An Indian rubber cord L metre long and area of cross-section A\[metr{{e}^{2}}\] is suspended vertically. Density of rubber is D \[kg/metr{{e}^{3}}\] and Young's modulus of rubber is E \[newton/metr{{e}^{2}}\]. If the wire extends by l metre under its own weight, then extension l is
  A)
              \[{{L}^{2}}Dg/E\] done clear
  B)
                \[{{L}^{2}}Dg/2E\] done clear
  C)
              \[{{L}^{2}}Dg/4E\] done clear
  D)
                L done clear
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• question_answer2)
  To break a wire, a force of \[{{10}^{6}}\,N/{{m}^{2}}\] is required. If the density of the material is \[3\times {{10}^{3}}\,kg/{{m}^{3}}\], then the length of the wire which will break by its own weight will be [Roorkee 1979; DPMT 2004]
  A)
  34 m    done clear
  B)
              30 m done clear
  C)
              300 m  done clear
  D)
              3 m done clear
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• question_answer3)
  Two rods of different materials having coefficients of linear expansion \[{{\alpha }_{1}},\,{{\alpha }_{2}}\] and Young's moduli \[{{Y}_{1}}\] and \[{{Y}_{2}}\] respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If \[{{\alpha }_{1}}:{{\alpha }_{2}}=2:3\], the thermal stresses developed in the two rods are equally provided \[{{Y}_{1}}:{{Y}_{2}}\] is equal to                         [IIT 1989]
  A)
  2 : 3     done clear
  B)
              1 : 1 done clear
  C)
              3 : 2     done clear
  D)
              4 : 9 done clear
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• question_answer4)
  The extension in a string obeying Hooke's law is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5x, the speed of sound will be [IIT 1996]
  A)
  1.22 v done clear
  B)
              0.61 v done clear
  C)
              1.50 v  done clear
  D)
              0.75 v done clear
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• question_answer5)
  One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight \[{{W}_{1}}\] is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height 3L/4 from its lower end is                           [IIT 1992]
  A)
              \[\frac{{{W}_{1}}}{S}\]       done clear
  B)
              \[\frac{{{W}_{1}}+(W/4)}{S}\] done clear
  C)
              \[\frac{{{W}_{1}}+(3W/4)}{S}\] done clear
  D)
                \[\frac{{{W}_{1}}+W}{S}\] done clear
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• question_answer6)
  There are two wires of same material and same length while the diameter of second wire is 2 times the diameter of first wire, then ratio of  extension produced in the wires by applying same load will be [DCE 2000; Roorkee 2000; DCE 2003]
  A)
  1 : 1     done clear
  B)
              2 : 1 done clear
  C)
              1 : 2     done clear
  D)
              4 : 1 done clear
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• question_answer7)
  A particle of mass m is under the influence of a force F which varies with the displacement x according to the relation \[F=-kx+{{F}_{0}}\]in which k and \[{{F}_{0}}\] are constants. The particle when disturbed will oscillate            [UPSEAT 2001]
  A)
  about \[x=0,\,\text{with }\omega \ne \sqrt{k/m}\] done clear
  B)
              about \[x=0,\,\text{with }\omega =\sqrt{k/m}\] done clear
  C)
              about \[x={{F}_{0}}/k\,\,\text{with }\omega =\sqrt{k/m}\] done clear
  D)
              about \[x={{F}_{0}}\text{/}k\,\text{with }\omega \ne \sqrt{k/m}\] done clear
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• question_answer8)
  An elastic material of Young's modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is                                [MP PET 1991; MP PMT 1990, 96; IIT 1992; AIIMS 1997]
  A)
              \[\frac{2Y}{{{S}^{2}}}\]    done clear
  B)
              \[\frac{{{S}^{2}}}{2Y}\] done clear
  C)
              \[\frac{S}{2Y}\]          done clear
  D)
              \[\frac{{{S}^{2}}}{Y}\] done clear
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