JEE Main & Advanced Physics Elasticity Question Bank

done Work Done in Stretching a Wire Total Questions - 30

• question_answer1)
  If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be                                              [CPMT 1976]
  A)
  V/25 done clear
  B)
                              5V done clear
  C)
                  V/5          done clear
  D)
                  25V done clear
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• question_answer2)
  The work done in stretching an elastic wire per unit volume is or strain energy in a stretched string is [NCERT 1981; EAMCET (Med.) 1995; MNR 1981; MP PET 1984; RPMT 1999; DCE 2003]
  A)
  Stress \[\times \] Strain          done clear
  B)
                  \[\frac{1}{2}\times \]Stress \[\times \]Strain done clear
  C)
                  \[2\times \text{strain}\times \text{stress}\]          done clear
  D)
                  Stress/Strain done clear
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• question_answer3)
  Calculate the work done, if a wire is loaded by 'Mg' weight and the increase in length is 'l' [CPMT 1999; DCE 1999, 2001; Pb. PET 2000, 01]
  A)
  Mgl          done clear
  B)
                  Zero done clear
  C)
                  Mgl/2      done clear
  D)
                  2Mgl done clear
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• question_answer4)
  Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be             [MP PET 1989]
  A)
  1 : 2        done clear
  B)
                  1 : 4 done clear
  C)
                  2 : 1        done clear
  D)
                  1 : 1 done clear
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• question_answer5)
  A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is    [MP PET 1989]
  A)
  Zero        done clear
  B)
                  0.05 joule done clear
  C)
                  100 joule done clear
  D)
                              500 joule done clear
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• question_answer6)
  If the force constant of a wire is K, the work done in increasing the length of the wire by l is      [MP PMT 1989]
  A)
  Kl/2         done clear
  B)
                  Kl done clear
  C)
                  \[K{{l}^{2}}/2\]  done clear
  D)
                  \[K{{l}^{2}}\] done clear
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• question_answer7)
  If the tension on a wire is removed at once, then
  A)
  It will break done clear
  B)
                              Its temperature will reduce done clear
  C)
                  There will be no change in its temperature done clear
  D)
                  Its temperature increases done clear
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• question_answer8)
  When strain is produced in a body within elastic limit, its internal energy
  A)
  Remains constant  done clear
  B)
                  Decreases done clear
  C)
                  Increases done clear
  D)
                              None of the above done clear
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• question_answer9)
  When shearing force is applied on a body, then the elastic potential energy is stored in it. On removing the force, this energy
  A)
  Converts into kinetic energy done clear
  B)
                  Converts into heat energy    done clear
  C)
                  Remains as potential energy done clear
  D)
                  None of the above done clear
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• question_answer10)
  A brass rod of cross-sectional area \[1\,c{{m}^{2}}\] and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Young's modulus of elasticity of brass is \[1\times {{10}^{11}}\,N/{{m}^{2}}\] and \[g=10\,m/{{\sec }^{2}}\], then increase in the energy of the rod will be                                                            [MP PMT 1991]
  A)
                  \[{{10}^{-5}}\]J done clear
  B)
                  \[2.5\times {{10}^{-5}}\]J done clear
  C)
                  \[5\times {{10}^{-5}}\]J done clear
  D)
                              \[2.5\times {{10}^{-4}}\]J done clear
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• question_answer11)
  If one end of a wire is fixed with a rigid support and the other end is stretched by a force of 10 N, then the increase in length is 0.5 mm. The ratio of the energy of the wire and the work done in displacing it through 1.5 mm by the weight is
  A)
                  \[\frac{1}{3}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  1 done clear
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• question_answer12)
  A wire is suspended by one end. At the other end a weight equivalent to 20 N force is applied. If the increase in length is 1.0 mm, the increase in energy of the wire will be
  A)
  0.01 J done clear
  B)
                              0.02 J done clear
  C)
                  0.04 J     done clear
  D)
                  1.00 J done clear
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• question_answer13)
  In the above question, the ratio of the increase in energy of the wire to the decrease in gravitational potential energy when load moves downwards by 1 mm, will be
  A)
  1              done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  \[\frac{1}{2}\] done clear
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• question_answer14)
  The Young's modulus of a wire is Y.  If the energy per unit volume is E, then the strain will be
  A)
                  \[\sqrt{\frac{2E}{Y}}\] done clear
  B)
                  \[\sqrt{2EY}\] done clear
  C)
                  EY           done clear
  D)
                  \[\frac{E}{Y}\] done clear
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• question_answer15)
  The ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be
  A)
  3 : 2        done clear
  B)
                  2 : 3 done clear
  C)
                  3 : 4        done clear
  D)
                  4 : 3 done clear
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• question_answer16)
  The length of a rod is 20 cm and area of cross-section \[2\,c{{m}^{2}}\]. The Young's modulus of the material of wire is \[1.4\times {{10}^{11}}\,N/{{m}^{2}}\]. If the rod is compressed by 5 kg-wt along its length, then increase in the energy of the rod in joules will be
  A)
                  \[8.57\times {{10}^{-6}}\] done clear
  B)
                              \[22.5\times {{10}^{-4}}\] done clear
  C)
                  \[9.8\times {{10}^{-5}}\] done clear
  D)
                              \[45.0\times {{10}^{-5}}\] done clear
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• question_answer17)
  If a spring extends by x on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)                                        [AIIMS 1997]
  A)
                  \[\frac{{{T}^{2}}}{2x}\]   done clear
  B)
                  \[\frac{{{T}^{2}}}{2k}\] done clear
  C)
                  \[\frac{2x}{{{T}^{2}}}\]   done clear
  D)
                  \[\frac{2{{T}^{2}}}{k}\] done clear
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• question_answer18)
  On stretching a wire, the elastic energy stored per unit volume is                                   [MP PMT/PET 1988]
  A)
                  \[Fl/2AL\] done clear
  B)
                  \[FA/2L\] done clear
  C)
                  \[FL/2A\] done clear
  D)
                              \[FL/2\] done clear
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• question_answer19)
  When a force is applied on a wire of uniform cross-sectional area \[3\times {{10}^{-6}}\,{{m}^{2}}\]and length 4m, the increase in length is 1 mm. Energy stored in it will be \[(Y=2\times {{10}^{11}}\,N/{{m}^{2}})\] [MP PET 1995; Pb. PET 2002]
  A)
  6250 J                    done clear
  B)
                  0.177 J done clear
  C)
                  0.075 J done clear
  D)
                              0.150 J done clear
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• question_answer20)
  K is the force constant of a spring. The work done in increasing its extension from \[{{l}_{1}}\] to \[{{l}_{2}}\] will be [MP PET 1995; MP PMT 1996]
  A)
                  \[K({{l}_{2}}-{{l}_{1}})\]  done clear
  B)
                  \[\frac{K}{2}({{l}_{2}}+{{l}_{1}})\] done clear
  C)
                  \[K(l_{2}^{2}-l_{1}^{2})\] done clear
  D)
                              \[\frac{K}{2}(l_{2}^{2}-l_{1}^{2})\] done clear
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• question_answer21)
  When a 4 kg mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by 5 cms will be \[(g=9.8\,metres/sex{{c}^{2}})\] [MP PMT 1995]
  A)
  4.900 joule            done clear
  B)
                  2.450 joule done clear
  C)
                  0.495 joule done clear
  D)
                              0.245 joule done clear
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• question_answer22)
  A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. It is stretched by an amount x. The work done is                 [MP PET 1996; BVP 2003; UPSEAT 2001]
  A)
                  \[\frac{YxA}{2L}\] done clear
  B)
                  \[\frac{Y{{x}^{2}}A}{L}\] done clear
  C)
                  \[\frac{Y{{x}^{2}}A}{2L}\]              done clear
  D)
                  \[\frac{2Y{{x}^{2}}A}{L}\] done clear
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• question_answer23)
  The elastic energy stored in a wire of Young's modulus Y is [MP PMT 1999]
  A)
                              \[Y\times \frac{\text{Strai}{{\text{n}}^{\text{2}}}}{\text{Volume}}\] done clear
  B)
                  Stress \[\times \] Strain \[\times \] Volume done clear
  C)
                  \[\frac{\text{Stres}{{\text{s}}^{\text{2}}}\times \text{Volume}}{2Y}\] done clear
  D)
                  \[\frac{1}{2}Y\times \] Stress \[\times \] Strain \[\times \] Volume done clear
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• question_answer24)
  A wire of length 50 cm and cross sectional area of 1 sq. mm is extended by 1 mm. The required work will be \[(Y=2\times {{10}^{10}}\,N{{m}^{-2}})\]                                       [RPET 1999]
  A)
                  \[6\times {{10}^{-2}}\,J\] done clear
  B)
                              \[4\times {{10}^{-2}}\,J\] done clear
  C)
                  \[2\times {{10}^{-2}}\,J\] done clear
  D)
                              \[1\times {{10}^{-2}}\,J\] done clear
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• question_answer25)
  The work per unit volume to stretch the length by 1% of a wire with cross sectional area of \[1\,m{{m}^{2}}\] will be. \[[Y=9\times {{10}^{11}}\,N/{{m}^{2}}]\]                                       [RPET 1999]
  A)
              \[9\times {{10}^{11}}\,J\] done clear
  B)
                       \[4.5\times {{10}^{7}}\,J\] done clear
  C)
              \[9\times {{10}^{7}}J\] done clear
  D)
                       \[4.5\times {{10}^{11}}\,J\] done clear
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• question_answer26)
  When load of 5kg is hung on a wire then extension of 3m takes place, then work done will be           [RPMT 2000]
  A)
  75 joule done clear
  B)
                       60 joule done clear
  C)
              50 joule done clear
  D)
                       100 joule done clear
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• question_answer27)
  A stretched rubber has                         [AIIMS 2000]
  A)
  Increased kinetic energy done clear
  B)
              Increased potential energy done clear
  C)
              Decreased kinetic energy done clear
  D)
              Decreased potential energy done clear
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• question_answer28)
  Which of the following is true for elastic potential energy density                                 [RPET 2001]
  A)
  Energy density = \[\frac{1}{2}\times \text{strain}\times \text{stress}\] done clear
  B)
              Energy density = \[{{\text{(strain)}}^{2}}\times \text{volume}\] done clear
  C)
              Energy density = (strain)× volume done clear
  D)
              Energy density = (stress)× volume done clear
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• question_answer29)
  A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm Then the elastic energy stored in the wire is                                  [AIEEE 2003]
  A)
  0.1 J    done clear
  B)
              0.2 J done clear
  C)
              10 J     done clear
  D)
              20 done clear
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• question_answer30)
  Wires A and B are made from the same material. A has twice the diameter and three times the length of B. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in A to that in B is [Kerala PMT 2004]
  A)
  2 : 3     done clear
  B)
              3 : 4     done clear
  C)
              3 : 2     done clear
  D)
              6 : 1 done clear
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