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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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