JEE Main & Advanced Physics Wave Mechanics Question Bank

done Self Evaluation Test - Mechanical Properties of Solids Total Questions - 80

• question_answer1)
  What per cent of length of wire increases by applying a stress of 1 kg \[weight/m{{m}^{2}}\] on it? \[(Y=1\times {{10}^{11}}N/{{m}^{2}}\,and\,1kg\,\,weight=9.8newton)\]
  A)
  0.0067% done clear
  B)
  0.0098% done clear
  C)
  0.0088% done clear
  D)
  0.0078% done clear
  View Solution play_arrow

• question_answer2)
  An elevator cable is to have a maximum stress of \[7\times {{10}^{7}}N/{{m}^{2}}\] to allow for appropriate safety factors. Its maximum upward acceleration is\[1.5m/{{s}^{2}}\]. If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross-section of the cable should be     
  A)
  \[3.28c{{m}^{2}}\] done clear
  B)
  \[2.28c{{m}^{2}}\] done clear
  C)
  \[0.328c{{m}^{2}}\] done clear
  D)
  \[0.823c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer3)
  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
  A)
  34m done clear
  B)
  30m done clear
  C)
  300m done clear
  D)
  3m done clear
  View Solution play_arrow

• question_answer4)
  A rubber cord catapult has cross-sectional area \[25\,m{{m}^{2}}\]and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5gm. taking\[{{Y}_{rubber}}=5\times {{10}^{8}}N/{{m}^{2}}\]. Velocity of projected missile is
  A)
  \[20m{{s}^{-1}}\]          done clear
  B)
         \[100m{{s}^{-1}}\] done clear
  C)
  \[250m{{s}^{-1}}\]        done clear
  D)
         \[200m{{s}^{-1}}\] done clear
  View Solution play_arrow

• question_answer5)
  Which of the following affects the elasticity of a substance?
  A)
  Change in temperature done clear
  B)
  Hammering and annealing done clear
  C)
  Impurity in substance done clear
  D)
  All of the above done clear
  View Solution play_arrow

• question_answer6)
  A metal wire of length L is suspended vertically from a rigid support when the body of mass M is attached to the lower end of the wire, the elongation of the wire is\[l\]. The elastic potential energy stored in the wire is
  A)
  \[mgl\] done clear
  B)
  \[mgl/2\] done clear
  C)
  \[mgl/3\] done clear
  D)
  \[mgl/4\] done clear
  View Solution play_arrow

• question_answer7)
  A body of mass 10 kg is attached to a wire of radius 3 cm. Its breaking stress is\[4.8\times {{10}^{7}}N{{m}^{-2}}\], the area of cross-section of the wire is\[{{10}^{-6}}{{m}^{2}}\] . What is the maximum angular velocity with which it can be rotated in the horizontal circle?
  A)
  \[1\,rad{{\sec }^{-1}}\] done clear
  B)
  \[2\,rad{{\sec }^{-1}}\] done clear
  C)
  \[4\,rad{{\sec }^{-1}}\] done clear
  D)
  \[8\,rad{{\sec }^{-1}}\] done clear
  View Solution play_arrow

• question_answer8)
  For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is
  A)
  \[3:\pi \] done clear
  B)
  \[\pi :3\] done clear
  C)
  \[1:\pi \] done clear
  D)
  \[\pi :1\] done clear
  View Solution play_arrow

• question_answer9)
  The length of a metal is \[{{\ell }_{1}}\] when the tension in it is\[{{T}_{1}}\]and is\[{{\ell }_{2}}\]when the tension is\[{{T}_{2}}\]. The original length of the wire is
  A)
  \[\frac{{{\ell }_{1}}+{{\ell }_{2}}}{2}\] done clear
  B)
  \[\frac{{{\ell }_{1}}{{T}_{2}}+{{\ell }_{2}}{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}}\] done clear
  C)
  (c)\[\frac{{{\ell }_{1}}{{T}_{2}}-{{\ell }_{2}}{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}}\] done clear
  D)
  \[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\] done clear
  View Solution play_arrow

• question_answer10)
  A light rod of length 2m suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight W is hung from a light rod as shown in figure. The rod hung by means of a steel wire of cross-sectional area \[{{A}_{1}}=0.1c{{m}^{2}}\] and brass wire of cross sectional area\[{{A}_{2}}=0.2c{{m}^{2}}\]. To have equal stress in both \[{{T}_{1}}/{{T}_{2}}=\] 
  A)
  1/3 done clear
  B)
  1/4                done clear
  C)
  4/3 done clear
  D)
  1/2           done clear
  View Solution play_arrow

• question_answer11)
  For an equal stretching force F, the young's modulus\[({{Y}_{s}})\] for steel and rubber\[({{Y}_{r}})\]are related as
  A)
  \[{{Y}_{s}}={{Y}_{r}}\] done clear
  B)
  \[{{Y}_{s}}<{{Y}_{r}}\] done clear
  C)
  \[{{Y}_{s}}>{{Y}_{r}}\] done clear
  D)
  \[{{Y}_{s}}\ge {{Y}_{r}}\] done clear
  View Solution play_arrow

• question_answer12)
  Which of the following is correct for young's modulus of elasticity\[(\gamma )?\][where \[r=\]radius of cross section of wire, \[l=\]length of wire]
  A)
  \[\gamma \propto {{r}^{2}}\] done clear
  B)
  \[\gamma \propto {{l}^{3}}\] done clear
  C)
  \[\gamma \propto l/{{r}^{2}}\] done clear
  D)
  \[\gamma \propto {{l}^{2}}\] done clear
  View Solution play_arrow

• question_answer13)
  If the length of a wire is reduced to half, then it can hold the
  A)
  Half load done clear
  B)
  same load done clear
  C)
  Double load done clear
  D)
  one fourth load done clear
  View Solution play_arrow

• question_answer14)
  A 2 m long rod of radius 1 cm which is fixed from one end is given a force of 8 N. The longitudinal strain developed will [\[take\,\gamma =2.5\times {{10}^{11}}N/{{m}^{2}}\]]
  A)
  \[{{10}^{-8}}\] done clear
  B)
  \[{{10}^{-6}}\] done clear
  C)
  \[{{10}^{-5}}\]            done clear
  D)
  \[{{10}^{-4}}\] done clear
  View Solution play_arrow

• question_answer15)
  A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find the strain. [Young's modulus of The meta\[=2\times {{10}^{11}}N/{{m}^{2}}\]]
  A)
  \[4\times {{10}^{-6}}\] done clear
  B)
  \[3\times {{10}^{-8}}\] done clear
  C)
  \[2\times {{10}^{-9}}\] done clear
  D)
  \[6\times {{10}^{-8}}\] done clear
  View Solution play_arrow

• question_answer16)
    The graph given is a stress-strain curve for
  A)
  Elastic objects     done clear
  B)
  plastics         done clear
  C)
  Elastomers     done clear
  D)
         None of these            done clear
  View Solution play_arrow

• question_answer17)
  If the ratio of radii of two wires of same material is 3 : 1 and ratio of their lengths is 5 : 1, then the ratio of the normal forces that will produce the same extension in the length of two wires is
  A)
  2:1  done clear
  B)
  4:1   done clear
  C)
  1:4  done clear
  D)
  1:1 done clear
  View Solution play_arrow

• question_answer18)
  An iron bar of length \[\ell \] cm and cross section A \[c{{m}^{2}}\]is pulled by a force of F dynes from ends so as to produce an elongation \[\Delta \ell \] cm. Which of the following statement is correct?
  A)
  Elongation is inversely proportional to length done clear
  B)
  Elongation is directly proportional to cross section A done clear
  C)
  Elongation is inversely proportional to cross-section done clear
  D)
  Elongation is directly proportional to Young's modulus done clear
  View Solution play_arrow

• question_answer19)
  Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is             
  A)
  Four times for wire A as for wire B done clear
  B)
  Twice for wire A as for wire B done clear
  C)
  Half for wire A as for wire B done clear
  D)
  One-fourth for wire A as for wire B done clear
  View Solution play_arrow

• question_answer20)
  A beam of metal supported at the two edges is loaded at the centre. The depression at the centre is proportional to        
  A)
    \[{{Y}^{2}}\] done clear
  B)
  Y    done clear
  C)
  1/Y done clear
  D)
  \[1/{{Y}^{2}}\] done clear
  View Solution play_arrow

• question_answer21)
  A steel ring of radius r and cross-section area 'A? is fitted on to a wooden disc of radius R(R > r). If Young's modulus be E, then the force with which the steel ring is expanded is
  A)
  \[AE\frac{R}{r}\] done clear
  B)
  \[AE\left( \frac{R-r}{r} \right)\] done clear
  C)
  \[\frac{E}{A}\left( \frac{R-r}{A} \right)\] done clear
  D)
  \[\frac{Er}{Ar}\] done clear
  View Solution play_arrow

• question_answer22)
  The adjacent graph shows the extension\[(\Delta l)\] of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. if the cross-sectional area of the wire is  \[{{10}^{-6}}{{m}^{2}}\], calculate the Young's modulus of the material of the wire      
  A)
  \[2\times {{10}^{11}}N/{{m}^{2}}\] done clear
  B)
  \[2\times {{10}^{-11}}N/{{m}^{2}}\] done clear
  C)
  \[2\times {{10}^{-12}}N/{{m}^{2}}\] done clear
  D)
  \[2\times {{10}^{-13}}N/{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer23)
  Two persons pull a rope towards themselves. Each person exerts a force of 100 N on the rope. Find the Young's modulus of the material of the rope if it extends in length by 1 cm. Original length of the rope = 2 m and the area of cross section \[2c{{m}^{2}}\]
  A)
  \[{{10}^{8}}N/{{m}^{2}}\] done clear
  B)
  \[{{10}^{7}}N/{{m}^{2}}\] done clear
  C)
  \[{{10}^{6}}N/{{m}^{2}}\] done clear
  D)
  \[{{10}^{5}}N/{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer24)
  If stress/strain is x in eastic region and y in the region of yield, then
  A)
  \[x=y\] done clear
  B)
  \[x>y\] done clear
  C)
  \[x<y\] done clear
  D)
  \[x=2y\] done clear
  View Solution play_arrow

• question_answer25)
  A metallic rod breaks when strain produced is 0.2%. The Young's modulus of the material of the rod is\[7\times {{10}^{9}}N/{{m}^{2}}\]. What should be its area of cross-section to support a load of 104 N?
  A)
  \[7.1\times {{10}^{-8}}{{m}^{2}}\] done clear
  B)
  \[7.1\times {{10}^{-6}}{{m}^{2}}\] done clear
  C)
  \[7.1\times {{10}^{-4}}{{m}^{2}}\] done clear
  D)
  \[7.1\times {{10}^{-2}}{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer26)
  A steel wire of original length 1 m and cross- sectional area \[4.00m{{m}^{2}}\] is clamped at the two ends so that it lies horizontally and without tension. If a load of 2.16 kg is suspended from the middle point of the wire, what would be its vertical depression? Y of the steel\[-2.0\times {{10}^{11}}N/{{m}^{2}}\]. Take \[g=10m/{{s}^{2}}\]
  A)
  1.5 cm done clear
  B)
  2.8cm done clear
  C)
  3.2 on done clear
  D)
  4.1cm done clear
  View Solution play_arrow

• question_answer27)
  Two wires are made of the same material and have the same volume. However first wire has cross- sectional area A and second wire has cross- sectional area 5A. If the length of first wire increases by \[\Delta l\] on applying force f, how much force is needed to stretch second wire by the same amount?
  A)
  \[14f\] done clear
  B)
  \[6f\]    done clear
  C)
  \[25f\] done clear
  D)
  \[9f\] done clear
  View Solution play_arrow

• question_answer28)
  One end of 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. Ifs is the area of cross section of the wire, the stress in the wire at a height\[\left( \frac{3L}{4} \right)\] from its lower end is
  A)
  \[\frac{{{W}_{1}}}{s}\] done clear
  B)
  \[\left[ {{W}_{1}}+\frac{W}{4} \right]s\] done clear
  C)
  \[\left[ {{W}_{1}}+\frac{3W}{4} \right]/s\] done clear
  D)
  \[\frac{{{W}_{1}}+W}{s}\] done clear
  View Solution play_arrow

• question_answer29)
  The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
  A)
  \[Length=50\text{ }cm,\text{ }diameter=0.5\text{ }mm\] done clear
  B)
  \[Length=100\text{ }cm,\text{ }diameter=1\text{ }mm\] done clear
  C)
  \[Length=200\text{ }cm,\text{ }diameter=2\text{ }mm\] done clear
  D)
  \[Length=300\text{ }cm,\text{ }diameter=3\text{ }mm.\] done clear
  View Solution play_arrow

• question_answer30)
  The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If \[{{Y}_{A}}\]and \[{{Y}_{B}}\] are the Young's moduli of the materials, then                 
  A)
  \[{{Y}_{B}}=2{{Y}_{A}}\] done clear
  B)
  \[{{Y}_{A}}={{Y}_{B}}\]  done clear
  C)
  \[{{Y}_{B}}=3{{Y}_{A}}\] done clear
  D)
  \[{{Y}_{A}}=3{{Y}_{B}}\] done clear
  View Solution play_arrow

• question_answer31)
  When forces are applied on a body such that it is still in static equilibrium, then the extent to which the body gets deformed, depends on
  A)
  Nature of the material done clear
  B)
  Magnitude of deforming force done clear
  C)
  Both [a] & [b] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  What is the minimum diameter of a brass rod if it is to support a 400N load without exceeding the elastic limit? Assume that the stress for the elastic limit is 379 MPa.
  A)
  1.16mm done clear
  B)
  2.32mm done clear
  C)
  0.16mm done clear
  D)
  1.35mm done clear
  View Solution play_arrow

• question_answer33)
  The elastic limit of steel is \[8\times {{10}^{8}}N/{{m}^{2}}\] and it?s Young's modulus\[2\times {{10}^{11}}N/{{m}^{2}}\]. Find the maximum elongation of a half-meter steel wire that can be given without exceeding the elastic limit.
  A)
  2mm done clear
  B)
  4mm done clear
  C)
  5mm done clear
  D)
  6mm done clear
  View Solution play_arrow

• question_answer34)
  A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of the stresses developed in the two wires and Y of steel\[=2\times {{10}^{11}}N/{{m}^{2}}\]. Y of copper\[=1.3\times {{10}^{11}}N/{{m}^{2}}\].
  A)
  1 done clear
  B)
  3      done clear
  C)
  5 done clear
  D)
  7 done clear
  View Solution play_arrow

• question_answer35)
  Two wires A and B of same material and of equal length with the radii in the ratio 1 : 2 are subjected to identical loads. If the length of A increases by 8 mm, then the increase in length of B is
  A)
  2mm done clear
  B)
  4mm done clear
  C)
  8mm done clear
  D)
  16mm done clear
  View Solution play_arrow

• question_answer36)
  The length of elastic string, obeying Hooke's law is \[{{\ell }_{1}}\]metres when the tension 4N and\[{{\ell }_{2}}\]metres when the tension is 5N. The length in metres when the tension is 9N is -
  A)
  \[5{{\ell }_{1}}-4{{\ell }_{2}}\] done clear
  B)
  \[5{{\ell }_{2}}-4{{\ell }_{1}}\] done clear
  C)
  \[9{{\ell }_{1}}-8{{\ell }_{2}}\] done clear
  D)
  \[9{{\ell }_{2}}-8{{\ell }_{1}}\] done clear
  View Solution play_arrow

• question_answer37)
  A steel wire of length / and cross section area A is stretched by 1 cm under a given load. When the same load is applied to another steel wire of double its length and half of its cross section area, the amount of stretching (extension) is
  A)
  0.5 cm done clear
  B)
  2cm done clear
  C)
  4cm      done clear
  D)
  1.5cm done clear
  View Solution play_arrow

• question_answer38)
  Two wires are made of the same material and have the same volume. However wire 1 has cross- sectional area A and wire 2 has cross-sectional area 9A. If the length of wire 1 increases by Ax on applying force F, how much force is needed to stretch wire 2 by the same amount?
  A)
  16F       done clear
  B)
  25 F done clear
  C)
  81 F      done clear
  D)
  64 F done clear
  View Solution play_arrow

• question_answer39)
  The force exerted by a special compression device is given as function of compression x as \[{{F}_{x}}(x)=kx(x-\ell )\] for\[0\le x\le \ell \], where \[\ell \]is maximum possible compression and A: is a constant. The force exerted by the device under compression is maximum when compression is -
  A)
  0 done clear
  B)
  \[\ell /4\]  done clear
  C)
  \[\ell /\sqrt{2}\] done clear
  D)
  \[\ell /2\] done clear
  View Solution play_arrow

• question_answer40)
  A force of \[6\times {{10}^{6}}\text{ }N{{m}^{-2}}\]is required for breaking a material. Then density p of the material is\[3\times {{10}^{3}}kg\,{{m}^{-3}}\]. If the wire is to break under its own weight, the length of the wire made of that material should be (\[take\,g=10\,m{{s}^{-2}}\])
  A)
  20m done clear
  B)
  200m done clear
  C)
  100m done clear
  D)
  2000m done clear
  View Solution play_arrow

• question_answer41)
  A steel wire of cross-sectional area \[3\times {{10}^{-6}}{{m}^{2}}\] can with stand a maximum strain of\[{{10}^{-3}}\]. Young's modulus of steel is\[2\times {{10}^{11}}N/{{m}^{2}}\]. The maximum mass the wire can hold is:
  A)
  40kg done clear
  B)
  60kg done clear
  C)
  80kg done clear
  D)
  100kg done clear
  View Solution play_arrow

• question_answer42)
  A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is\[2\times {{10}^{11}}N{{m}^{-2}}\]. The percentage strain is about
  A)
  0.16% done clear
  B)
  0.32% done clear
  C)
  0.08% done clear
  D)
  0.24%43 done clear
  View Solution play_arrow

• question_answer43)
  A thick rope of density \[\rho \]and length L is hung from a rigid support. The Young's modulus of the material of rope is Y. The increase in length of the rope due to its own weight is
  A)
  \[(1/4)\rho g{{L}^{2}}/Y\] done clear
  B)
  \[(1/2)\rho g{{L}^{2}}/Y\] done clear
  C)
  \[\rho g{{L}^{2}}/Y\] done clear
  D)
  \[\rho gL/Y\] done clear
  View Solution play_arrow

• question_answer44)
  If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is :             
  A)
  \[\frac{3c}{2a{{b}^{2}}}\] done clear
  B)
  \[\frac{2{{a}^{2}}c}{b}\] done clear
  C)
  \[\frac{3a}{2{{b}^{2}}c}\] done clear
  D)
  \[\frac{2ac}{{{b}^{2}}}\] done clear
  View Solution play_arrow

• question_answer45)
  What per cent of length of wire increases by applying a stress of 1 kg weight/ \[m{{m}^{2}}\]on it? (\[(Y=1\times {{10}^{11}}N/{{m}^{2}}\]and 1 kg weight\[=9.8\] newton)
  A)
  0.0067% done clear
  B)
  0.0098% done clear
  C)
  0.0088% done clear
  D)
  0.0078% done clear
  View Solution play_arrow

• question_answer46)
  A metal wire of length \[{{L}_{1}}\]and area of cross-section A is attached to a rigid support. Another metal wire of length \[{{L}_{2}}\] and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If \[{{Y}_{1}}\]and \[{{Y}_{2}}\] are the young's moduli of the wires respectively, the effective force constant of the system of two wires is                 
  A)
  \[\frac{({{Y}_{1}}{{Y}_{2}})A}{2({{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}})}\] done clear
  B)
  \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{({{L}_{1}}{{L}_{2}})}^{1/2}}}\] done clear
  C)
  \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}}}\] done clear
  D)
  \[\frac{{{({{Y}_{1}}{{Y}_{2}})}^{1/2}}A}{{{({{L}_{2}}{{L}_{1}})}^{1/2}}}\] done clear
  View Solution play_arrow

• question_answer47)
  A steel wire 1.5 m long and of radius 1 mm is attached with a load 3 kg at one end the other end of the wire is fixed. It is whirled in a vertical circle with a frequency 2 Hz. Find the elongation of the wire when the weight is at the lowest position. [\[Y=2\times {{10}^{11}}N/{{m}^{2}}\,\,\,\,\,\,g=10m{{s}^{-2}}\]]
  A)
  \[1.77\times {{10}^{-3}}m\] done clear
  B)
  \[7.17\times {{10}^{-3}}m\] done clear
  C)
  \[3.17\times {{10}^{-7}}m\] done clear
  D)
  \[1.37\times {{10}^{-7}}m\] done clear
  View Solution play_arrow

• question_answer48)
  A platform is suspended by four wires at its corners. The wires are 3m long and have a diameter of 2.0mm. Young's modulus for the material of the wires is 1,80,000 MPa. How far will the platform drop (due to elongation of the wires) if a 50 kg load is placed at the centre of the platform?           
  A)
  0.25 mm done clear
  B)
  0.65 mm done clear
  C)
  1.65 mm done clear
  D)
  0.35 mm done clear
  View Solution play_arrow

• question_answer49)
  A force of \[{{10}^{3}}\] newton, stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimetre is
  A)
  \[4\times {{10}^{3}}N\] done clear
  B)
  \[16\times {{10}^{3}}N\] done clear
  C)
  \[\frac{1}{4}\times {{10}^{3}}N\] done clear
  D)
  \[\frac{1}{16}\times {{10}^{3}}N\] done clear
  View Solution play_arrow

• question_answer50)
  A copper wire of length 1.0m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. If the Young's modulii of copper and steel are respectively \[1.0\times {{10}^{11}}N{{m}^{-2}}\] and \[2.0\times {{10}^{11}}N{{m}^{-2}}\], the total extension of the composite wire is:
  A)
  1.75 mm done clear
  B)
  2.0 mm done clear
  C)
  1.50 mm done clear
  D)
  1.25 mm done clear
  View Solution play_arrow

• question_answer51)
  The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that:                                     
  A)
  A is brittle but B is ductile   done clear
  B)
  A is ductile and B is brittle done clear
  C)
  Both A and B are ductile     done clear
  D)
  Both A and B are brittle     done clear
  View Solution play_arrow

• question_answer52)
  A square frame of ABCD consisting of five steel bars of cross section area 400 \[m{{m}^{2}}\] and joined by pivot is subjected to action of two forces \[P=40\text{ }kN\]in the direction of the diagonal as shown. Find change in angle at A if Young's modulus \[Y=2\times {{10}^{5}}N/\min \]
  A)
  \[\frac{1}{2000}rad\] done clear
  B)
  \[\frac{1}{1000}rad\] done clear
  C)
  \[\frac{\sqrt{2}}{1000}rad\] done clear
  D)
  none done clear
  View Solution play_arrow

• question_answer53)
  A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values Rand 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal: 
  A)
  \[L\left( 1+\frac{2}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] done clear
  B)
  \[L\left( 1+\frac{1}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] done clear
  C)
  \[L\left( 1+\frac{1}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] done clear
  D)
  \[L\left( 1+\frac{2}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] done clear
  View Solution play_arrow

• question_answer54)
  Which of the following is the correct relation? \[Y=\]Young's modulus & \[G=\]modulus of rigidity?
  A)
  \[Y<G\] done clear
  B)
  \[Y>G\] done clear
  C)
  \[Y=G\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer55)
  The ratio of shearing stress to the corresponding shearing strain is called
  A)
  Bulk modulus done clear
  B)
  Young's modulus done clear
  C)
  Modulus of rigidity done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer56)
  Two rods A and B of the same material and length have their radii \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio \[\left( \frac{Angle\,of\,twist\,at\,the\,end\,of\,A}{Angle\,of\,twist\,at\,the\,end\,of\,B} \right)\]
  A)
  \[r_{1}^{2}/r_{2}^{2}\] done clear
  B)
  \[r_{1}^{3}/r_{2}^{3}\] done clear
  C)
  \[r_{2}^{4}/r_{1}^{4}\] done clear
  D)
  \[r_{1}^{4}/r_{2}^{4}\] done clear
  View Solution play_arrow

• question_answer57)
  A metallic wire of length 2.0 m is elongated by 2.0 mm. Area of cross-section of the wire is 4.0 mm2. The elastic potential energy stored in the wire in elongated condition is [young's modulus of the metallic wire is \[=2\times {{10}^{11}}N/{{m}^{2}}\]]
  A)
  8.23 done clear
  B)
  0.83   done clear
  C)
  6.23 done clear
  D)
  0.63 done clear
  View Solution play_arrow

• question_answer58)
  When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in \[dyne/c{{m}^{2}}\] is
  A)
  \[10\times {{10}^{12}}\] done clear
  B)
  \[100\times {{10}^{12}}\] done clear
  C)
  \[1\times {{10}^{12}}\] done clear
  D)
  \[10\times {{10}^{12}}\] done clear
  View Solution play_arrow

• question_answer59)
  A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is
  A)
  0.01  done clear
  B)
  0.06  done clear
  C)
  0.02  done clear
  D)
  0.03 done clear
  View Solution play_arrow

• question_answer60)
  When a 4 kg mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by 2cms. The work required to be done by an external agent in stretching this spring by 5cms will be \[(g=9.8\text{ }m/se{{c}^{2}})\]
  A)
  4.900joule done clear
  B)
  2.450joule done clear
  C)
  0.495 joule done clear
  D)
  0.245 joule done clear
  View Solution play_arrow

• question_answer61)
  Consider four steel wires of dimensions given below (d = diameter and / = length): \[l=1m,d=1mm\] \[l=2m,d=2mm\] \[l=2m,d=1mm\] \[l=1m,d=2mm\] If same force is applied to all the wires then the elastic potential energy stored will be maximum in wire:       
  A)
  A done clear
  B)
  B     done clear
  C)
  C done clear
  D)
  D done clear
  View Solution play_arrow

• question_answer62)
  If in a wire of Young's modulus Y, longitudinal strain X is produced, then the value of potential energy stored in its unit volume will be
  A)
  \[Y{{X}^{2}}\] done clear
  B)
  \[2Y{{X}^{2}}\] done clear
  C)
  \[{{Y}^{2}}X/2\] done clear
  D)
  \[Y{{X}^{2}}/2\] done clear
  View Solution play_arrow

• question_answer63)
  The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is:
  A)
  1%  done clear
  B)
  2%   done clear
  C)
  2.5% done clear
  D)
  4% done clear
  View Solution play_arrow

• question_answer64)
  A material has poisson?s ratio 0.50. If a uniform rod of it suffers a longitudinal strain of \[2\times {{10}^{-3}}\], then the percentage change in volume is
  A)
  0.6 done clear
  B)
  0.4    done clear
  C)
  02 done clear
  D)
  Zero done clear
  View Solution play_arrow

• question_answer65)
  The system is rotated with angular speed ox. (see figure). What is the ratio of energy stored in each wire?                
  A)
  31:9 done clear
  B)
  50:9   done clear
  C)
  47:9 done clear
  D)
  8:9   done clear
  View Solution play_arrow

• question_answer66)
  When a force is applied on a wire of uniform cross-section area \[3\times {{10}^{-6}}{{m}^{2}}\] and length 4m, the increase in length is 1 mm. Energy stored in it will be (\[Y=2\times {{10}^{11}}N/{{m}^{2}}\])
  A)
  6250J done clear
  B)
  0.177J done clear
  C)
  0.075 J done clear
  D)
  0.150J done clear
  View Solution play_arrow

• question_answer67)
  A metal rod of Young's modulus \[2\times {{10}^{10}}N{{m}^{-2}}\] undergoes an elastic strain of 0.06%. The energy  per unit volume stored in J m-3 is
  A)
  3600 done clear
  B)
  7200 done clear
  C)
  10800 done clear
  D)
  14400 done clear
  View Solution play_arrow

• question_answer68)
  When the load on a wire is increasing slowly from 2 kg to 4 kg, the elongation increases from 0.6 mm to 1 mm. The work done during this extension of the wire is (\[g=10m/{{s}^{2}}\])
  A)
  \[9\times {{10}^{-3}}J\] done clear
  B)
  \[12\times {{10}^{-3}}J\] done clear
  C)
  \[14\times {{10}^{-3}}J\] done clear
  D)
  \[16\times {{10}^{-3}}J\] done clear
  View Solution play_arrow

• question_answer69)
  A solid cube is subjected to a pressure of \[5\times {{10}^{5}}N{{m}^{-2}}\].Each side of the cube is shortened by 1 %. Find x if \[1.67\times {{10}^{x}}N/{{m}^{2}}\] be the bulk modulus of elasticity of the cube.
  A)
  7                      done clear
  B)
  11    done clear
  C)
  12                     done clear
  D)
  15 done clear
  View Solution play_arrow

• question_answer70)
  Two parallel and opposite forces, each of magnitude 4000 N are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side. The angle of Shear is [shear modulas of metal is 80 G Pa]
  A)
  \[8\times {{10}^{-7}}rad\] done clear
  B)
  \[7\times {{10}^{-7}}rad\] done clear
  C)
  \[6\times {{10}^{-6}}rad\] done clear
  D)
  \[5\times {{10}^{-5}}ra\] done clear
  View Solution play_arrow

• question_answer71)
  Two Metal strips are riveted together at their ends by four rivets, each of diameter\[a=6\text{ }mm\]. The maximum tension that can be exerted by the riveted strip (if the Shearing stress on the rivet is not to exceed\[6.9\times \text{1}{{\text{0}}^{7}}Pa\]) is?
  A)
  \[6.8\times {{10}^{2}}N\]  done clear
  B)
  \[7.8\times {{10}^{3}}N\] done clear
  C)
  \[8.28\times {{10}^{4}}N\] done clear
  D)
  \[9.1\times {{10}^{3}}N\] done clear
  View Solution play_arrow

• question_answer72)
  Two cylinders A and B of the same material have same length, their radii being in the ratio 1:2 respectively. The two are joined end to end as shown. One end of cylinder A is rigidly clamped while free end of cylinder B is twisted through an angle 9. The angle of twist of cylinder A is           
  A)
  \[\frac{16}{17}\theta \] done clear
  B)
  \[\frac{15}{16}\theta \] done clear
  C)
  \[8\theta \] done clear
  D)
  \[\frac{3}{2}\theta \] done clear
  View Solution play_arrow

• question_answer73)
  The pressure in an explosion chamber is 345 MPa. What would be the percent change in volume of a piece of copper subjected to this pressure? The bulk modulus for copper is 138 \[Gpa\]\[(=138\times {{10}^{9}}Pa)\] 
  A)
  0.1% done clear
  B)
  0.5% done clear
  C)
  0.25% done clear
  D)
  0.2% done clear
  View Solution play_arrow

• question_answer74)
  The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is
  A)
  \[\frac{B}{3p}\] done clear
  B)
  \[\frac{3p}{B}\] done clear
  C)
  \[\frac{p}{3p}\] done clear
  D)
  \[\frac{p}{B}\] done clear
  View Solution play_arrow

• question_answer75)
  The Young's modulus of the material of a wire is \[2\times {{10}^{10}}N{{m}^{-2}}\]. If the elongation strain is 1 %, then the energy stored in the wire per unit volume in \[J{{m}^{-3}}\] is
  A)
  \[{{10}^{6}}\]  done clear
  B)
  \[{{10}^{8}}\] done clear
  C)
  \[2\times {{10}^{6}}\] done clear
  D)
  \[2\times {{10}^{8}}\] done clear
  View Solution play_arrow

• question_answer76)
  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 t mm. The energy stored in the wire due to stretching is
  A)
  Zero done clear
  B)
  0.05 joule done clear
  C)
  100 joule done clear
  D)
  500 joule done clear
  View Solution play_arrow

• question_answer77)
  A wire suspended vertically from one of its ends is stretched by attaching a weight of 200N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is
  A)
  0.2 J done clear
  B)
  10 J   done clear
  C)
  20 J done clear
  D)
  0.1 J done clear
  View Solution play_arrow

• question_answer78)
  Two, spring P and Q of force constants \[{{k}_{p}}\] and \[kQ\left( kQ=\frac{{{k}_{p}}}{2} \right)\] are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is
  A)
  E done clear
  B)
  2E    done clear
  C)
  E/2 done clear
  D)
  E/4 done clear
  View Solution play_arrow

• question_answer79)
  A spherical ball contracts in volume by 0.02% when subjected to a pressure of 100 atmosphere. Assuming one atmosphere \[={{10}^{5}}N{{m}^{-2}}\], the bulk modulus of the material of the ball is
  A)
  \[0.02\times {{10}^{5}}N/{{m}^{2}}\] done clear
  B)
  \[0.02\times {{10}^{7}}N/{{m}^{2}}\] done clear
  C)
  \[50\times {{10}^{7}}N/{{m}^{2}}\] done clear
  D)
  \[50\times {{10}^{9}}N/{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer80)
  A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up and recast into a solid rod of the same length. The ratio of the torsional rigidities of the circular tube and the solid rod is
  A)
  \[\frac{{{(8.02)}^{4}}-{{(7.98)}^{4}}}{{{(0.8)}^{4}}}\] done clear
  B)
  \[\frac{{{(8.02)}^{2}}-{{(7.98)}^{2}}}{{{(0.8)}^{2}}}\] done clear
  C)
  \[\frac{{{(0.8)}^{2}}}{{{(8.02)}^{4}}-{{(7.98)}^{4}}}\] done clear
  D)
  \[\frac{{{(0.8)}^{2}}}{{{(8.02)}^{3}}-{{(7.98)}^{2}}}\] done clear
  View Solution play_arrow