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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2051. |
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 |
| B. | 0.83 |
| C. | 6.23 |
| D. | 0.63 |
| Answer» C. 6.23 | |
| 2052. |
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. | \[r_{1}^{2}/r_{2}^{2}\] |
| B. | \[r_{1}^{3}/r_{2}^{3}\] |
| C. | \[r_{2}^{4}/r_{1}^{4}\] |
| D. | \[r_{1}^{4}/r_{2}^{4}\] |
| Answer» D. \[r_{1}^{4}/r_{2}^{4}\] | |
| 2053. |
Which of the following is the correct relation? \[Y=\]Young's modulus & \[G=\]modulus of rigidity? |
| A. | \[Y<G\] |
| B. | \[Y>G\] |
| C. | \[Y=G\] |
| D. | None of these |
| Answer» C. \[Y=G\] | |
| 2054. |
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. | \[\frac{1}{2000}rad\] |
| B. | \[\frac{1}{1000}rad\] |
| C. | \[\frac{\sqrt{2}}{1000}rad\] |
| D. | none |
| Answer» C. \[\frac{\sqrt{2}}{1000}rad\] | |
| 2055. |
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. | \[L\left( 1+\frac{2}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] |
| B. | \[L\left( 1+\frac{1}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] |
| C. | \[L\left( 1+\frac{1}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] |
| D. | \[L\left( 1+\frac{2}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] |
| Answer» D. \[L\left( 1+\frac{2}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\] | |
| 2056. |
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 |
| B. | A is ductile and B is brittle |
| C. | Both A and B are ductile |
| D. | Both A and B are brittle |
| Answer» C. Both A and B are ductile | |
| 2057. |
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 |
| B. | 2.0 mm |
| C. | 1.50 mm |
| D. | 1.25 mm |
| Answer» E. | |
| 2058. |
Which of the following affects the elasticity of a substance? |
| A. | Change in temperature |
| B. | Hammering and annealing |
| C. | Impurity in substance |
| D. | All of the above |
| Answer» E. | |
| 2059. |
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. | \[4\times {{10}^{3}}N\] |
| B. | \[16\times {{10}^{3}}N\] |
| C. | \[\frac{1}{4}\times {{10}^{3}}N\] |
| D. | \[\frac{1}{16}\times {{10}^{3}}N\] |
| Answer» C. \[\frac{1}{4}\times {{10}^{3}}N\] | |
| 2060. |
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 |
| B. | 0.65 mm |
| C. | 1.65 mm |
| D. | 0.35 mm |
| Answer» C. 1.65 mm | |
| 2061. |
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. | \[1.77\times {{10}^{-3}}m\] |
| B. | \[7.17\times {{10}^{-3}}m\] |
| C. | \[3.17\times {{10}^{-7}}m\] |
| D. | \[1.37\times {{10}^{-7}}m\] |
| Answer» B. \[7.17\times {{10}^{-3}}m\] | |
| 2062. |
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. | 0.000067 |
| B. | 0.000098 |
| C. | 0.000088 |
| D. | 0.000078 |
| Answer» C. 0.000088 | |
| 2063. |
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. | \[\frac{3c}{2a{{b}^{2}}}\] |
| B. | \[\frac{2{{a}^{2}}c}{b}\] |
| C. | \[\frac{3a}{2{{b}^{2}}c}\] |
| D. | \[\frac{2ac}{{{b}^{2}}}\] |
| Answer» D. \[\frac{2ac}{{{b}^{2}}}\] | |
| 2064. |
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. | \[(1/4)\rho g{{L}^{2}}/Y\] |
| B. | \[(1/2)\rho g{{L}^{2}}/Y\] |
| C. | \[\rho g{{L}^{2}}/Y\] |
| D. | \[\rho gL/Y\] |
| Answer» C. \[\rho g{{L}^{2}}/Y\] | |
| 2065. |
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. | 0.0016 |
| B. | 0.0032 |
| C. | 0.0008 |
| D. | 0.24%43 |
| Answer» B. 0.0032 | |
| 2066. |
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 |
| B. | 60kg |
| C. | 80kg |
| D. | 100kg |
| Answer» E. | |
| 2067. |
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 |
| B. | 200m |
| C. | 100m |
| D. | 2000m |
| Answer» C. 100m | |
| 2068. |
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. | \[20m{{s}^{-1}}\] |
| B. | \[100m{{s}^{-1}}\] |
| C. | \[250m{{s}^{-1}}\] |
| D. | \[200m{{s}^{-1}}\] |
| Answer» D. \[200m{{s}^{-1}}\] | |
| 2069. |
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 |
| B. | \[\ell /4\] |
| C. | \[\ell /\sqrt{2}\] |
| D. | \[\ell /2\] |
| Answer» E. | |
| 2070. |
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 |
| B. | 25 F |
| C. | 81 F |
| D. | 64 F |
| Answer» D. 64 F | |
| 2071. |
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. | \[5{{\ell }_{1}}-4{{\ell }_{2}}\] |
| B. | \[5{{\ell }_{2}}-4{{\ell }_{1}}\] |
| C. | \[9{{\ell }_{1}}-8{{\ell }_{2}}\] |
| D. | \[9{{\ell }_{2}}-8{{\ell }_{1}}\] |
| Answer» C. \[9{{\ell }_{1}}-8{{\ell }_{2}}\] | |
| 2072. |
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 |
| B. | 4mm |
| C. | 8mm |
| D. | 16mm |
| Answer» B. 4mm | |
| 2073. |
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 |
| B. | 3 |
| C. | 5 |
| D. | 7 |
| Answer» B. 3 | |
| 2074. |
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 |
| B. | 4mm |
| C. | 5mm |
| D. | 6mm |
| Answer» B. 4mm | |
| 2075. |
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 |
| B. | 2.32mm |
| C. | 0.16mm |
| D. | 1.35mm |
| Answer» B. 2.32mm | |
| 2076. |
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 |
| B. | Magnitude of deforming force |
| C. | Both [a] & [b] |
| D. | None of these |
| Answer» D. None of these | |
| 2077. |
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. | \[{{Y}_{B}}=2{{Y}_{A}}\] |
| B. | \[{{Y}_{A}}={{Y}_{B}}\] |
| C. | \[{{Y}_{B}}=3{{Y}_{A}}\] |
| D. | \[{{Y}_{A}}=3{{Y}_{B}}\] |
| Answer» E. | |
| 2078. |
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 |
| B. | 30m |
| C. | 300m |
| D. | 3m |
| Answer» B. 30m | |
| 2079. |
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. | \[14f\] |
| B. | \[6f\] |
| C. | \[25f\] |
| D. | \[9f\] |
| Answer» D. \[9f\] | |
| 2080. |
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 |
| B. | 2.8cm |
| C. | 3.2 on |
| D. | 4.1cm |
| Answer» B. 2.8cm | |
| 2081. |
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. | \[7.1\times {{10}^{-8}}{{m}^{2}}\] |
| B. | \[7.1\times {{10}^{-6}}{{m}^{2}}\] |
| C. | \[7.1\times {{10}^{-4}}{{m}^{2}}\] |
| D. | \[7.1\times {{10}^{-2}}{{m}^{2}}\] |
| Answer» D. \[7.1\times {{10}^{-2}}{{m}^{2}}\] | |
| 2082. |
If stress/strain is x in eastic region and y in the region of yield, then |
| A. | \[x=y\] |
| B. | \[x>y\] |
| C. | \[x<y\] |
| D. | \[x=2y\] |
| Answer» C. \[x<y\] | |
| 2083. |
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. | \[{{10}^{8}}N/{{m}^{2}}\] |
| B. | \[{{10}^{7}}N/{{m}^{2}}\] |
| C. | \[{{10}^{6}}N/{{m}^{2}}\] |
| D. | \[{{10}^{5}}N/{{m}^{2}}\] |
| Answer» B. \[{{10}^{7}}N/{{m}^{2}}\] | |
| 2084. |
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. | \[2\times {{10}^{11}}N/{{m}^{2}}\] |
| B. | \[2\times {{10}^{-11}}N/{{m}^{2}}\] |
| C. | \[2\times {{10}^{-12}}N/{{m}^{2}}\] |
| D. | \[2\times {{10}^{-13}}N/{{m}^{2}}\] |
| Answer» B. \[2\times {{10}^{-11}}N/{{m}^{2}}\] | |
| 2085. |
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. | \[AE\frac{R}{r}\] |
| B. | \[AE\left( \frac{R-r}{r} \right)\] |
| C. | \[\frac{E}{A}\left( \frac{R-r}{A} \right)\] |
| D. | \[\frac{Er}{Ar}\] |
| Answer» C. \[\frac{E}{A}\left( \frac{R-r}{A} \right)\] | |
| 2086. |
A beam of metal supported at the two edges is loaded at the centre. The depression at the centre is proportional to |
| A. | \[{{Y}^{2}}\] |
| B. | Y |
| C. | 1/Y |
| D. | \[1/{{Y}^{2}}\] |
| Answer» D. \[1/{{Y}^{2}}\] | |
| 2087. |
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. | \[3.28c{{m}^{2}}\] |
| B. | \[2.28c{{m}^{2}}\] |
| C. | \[0.328c{{m}^{2}}\] |
| D. | \[0.823c{{m}^{2}}\] |
| Answer» B. \[2.28c{{m}^{2}}\] | |
| 2088. |
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 |
| B. | Elongation is directly proportional to cross section A |
| C. | Elongation is inversely proportional to cross-section |
| D. | Elongation is directly proportional to Young's modulus |
| Answer» D. Elongation is directly proportional to Young's modulus | |
| 2089. |
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 |
| B. | 4:1 |
| C. | 1:4 |
| D. | 0.0423611111111111 |
| Answer» E. | |
| 2090. |
The graph given is a stress-strain curve for |
| A. | Elastic objects |
| B. | plastics |
| C. | Elastomers |
| D. | None of these |
| Answer» D. None of these | |
| 2091. |
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. | \[4\times {{10}^{-6}}\] |
| B. | \[3\times {{10}^{-8}}\] |
| C. | \[2\times {{10}^{-9}}\] |
| D. | \[6\times {{10}^{-8}}\] |
| Answer» B. \[3\times {{10}^{-8}}\] | |
| 2092. |
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. | \[{{10}^{-8}}\] |
| B. | \[{{10}^{-6}}\] |
| C. | \[{{10}^{-5}}\] |
| D. | \[{{10}^{-4}}\] |
| Answer» B. \[{{10}^{-6}}\] | |
| 2093. |
If the length of a wire is reduced to half, then it can hold the |
| A. | Half load |
| B. | same load |
| C. | Double load |
| D. | one fourth load |
| Answer» C. Double load | |
| 2094. |
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. | \[\gamma \propto {{r}^{2}}\] |
| B. | \[\gamma \propto {{l}^{3}}\] |
| C. | \[\gamma \propto l/{{r}^{2}}\] |
| D. | \[\gamma \propto {{l}^{2}}\] |
| Answer» D. \[\gamma \propto {{l}^{2}}\] | |
| 2095. |
For an equal stretching force F, the young's modulus\[({{Y}_{s}})\] for steel and rubber\[({{Y}_{r}})\]are related as |
| A. | \[{{Y}_{s}}={{Y}_{r}}\] |
| B. | \[{{Y}_{s}}<{{Y}_{r}}\] |
| C. | \[{{Y}_{s}}>{{Y}_{r}}\] |
| D. | \[{{Y}_{s}}\ge {{Y}_{r}}\] |
| Answer» D. \[{{Y}_{s}}\ge {{Y}_{r}}\] | |
| 2096. |
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. | 44256 |
| B. | 1/4 |
| C. | 44259 |
| D. | 1/2 |
| Answer» E. | |
| 2097. |
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. | 0.000067 |
| B. | 0.000098 |
| C. | 0.000088 |
| D. | 0.000078 |
| Answer» C. 0.000088 | |
| 2098. |
Two capillary of length L and 2L and of radius R and 2R are connected in series. The net rate of flow of fluid through them will be (given rate to the flow through single capillary, \[X=\frac{\pi P{{R}^{4}}}{8\eta L}\]) |
| A. | \[\frac{8}{9}X\] |
| B. | \[\frac{9}{8}X\] |
| C. | \[\frac{5}{7}X\] |
| D. | \[\frac{7}{5}X\] |
| Answer» B. \[\frac{9}{8}X\] | |
| 2099. |
A hollow sphere of mass \[M=50kg\]and radius\[r={{\left( \frac{3}{40\pi } \right)}^{1/3}}\]m is immersed in a tank of water (density \[{{\rho }_{w}}={{10}^{3}}kg/{{m}^{3}}\]). The sphere is tied to the bottom of a tank by two wires A and B as shown. Tension in wire A is\[(g=10m/{{s}^{2}})\] |
| A. | \[125\sqrt{2}N\] |
| B. | \[125N\] |
| C. | \[250\sqrt{2}N\] |
| D. | \[250N\] |
| Answer» D. \[250N\] | |
| 2100. |
Radius of a capillary is\[2\times {{10}^{-3}}m\]. A liquid of weight \[6.28\times {{10}^{-4}}N\] may remain in the capillary then the surface tension of liquid will be |
| A. | \[5\times {{10}^{-3}}N/m\] |
| B. | \[5\times {{10}^{-2}}N/m\] |
| C. | \[5N/m\] |
| D. | \[50N/m\] |
| Answer» C. \[5N/m\] | |