STD 11- Mechanical properties of solids PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 101 questions

51. 51. The elastic potential energy stored in a steel wire of length \(20\,m\) stretched through \(2 \,cm\) is \(80\,J\). The cross sectional area of the wire is \(.........\,mm ^2\) (Given, \(y =2.0 \times 10^{11}\,Nm ^{-2}\) ) 2023 Medium
52. 52. The length of wire becomes \(l_1\) and \(l_2\) when \(100\,N\) and \(120\,N\) tensions are applied respectively. If \(10l_2=11l_1\), the natural length of wire will be \(\frac{1}{x} l_1\). Here the value of \(x\) is ........ 2023 Medium
53. 53. The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is  (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\) 2023 Medium
54. 54. Two wires each of radius \(0.2\,cm\) and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is \(.........\times 10^{-6}\,m\). [Young's modulus for steel \(=2 \times 10^{11}\,Nm ^{-2}\) and \(g =10\,ms ^{-2}\) ]
    2023 Hard
55. 55. Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same] 2023 Medium
56. 56. A metal wire of length \(0.5 m\) and cross-sectional area \(10^{-4}\; m ^{2}\) has breaking stress \(5 \times 10^{8}\; Nm ^{-2}\). A block of \(10\; kg\) is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be \(ms ^{-1}\). 2022 Hard
57. 57. A square aluminium (shear modulus is \(25 \times 10^{9}\,Nm ^{-2}\) ) slab of side \(60\,cm\) and thickness \(15\,cm\) is subjected to a shearing force (on its narrow face) of \(18.0 \times 10^{4}\,N\). The lower edge is riveted to the floor. The displacement of the upper edge is \(.......\mu\,m\). 2022 Hard
58. 58. A steel wire of length \(3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)\) and a copper wire of length \(4.4\,M\) \(\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)\), both of radius \(1.4\,mm\) are connected end to end. When stretched by a load, the net elongation is found to be \(1.4\,mm\). The load applied, in Newton, will be. (Given \(\pi=\frac{22}{7}\)) 2022 Hard
59. 59. A string of area of cross-section \(4\,mm ^{2}\) and length \(0.5\) is connected with a rigid body of mass \(2\,kg\). The body is rotated in a vertical circular path of radius \(0.5\,m\). The body acquires a speed of \(5\,m / s\) at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is \(\ldots . . \times 10^{-5}\). (Use Young's modulus \(10^{11}\,N / m ^{2}\) and \(g =10\,m / s ^{2}\) ) 2022 Hard
60. 60. A uniform heavy rod of mass \(20\,kg\). Cross sectional area \(0.4\,m ^{2}\) and length \(20\,m\) is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is \(x \times 10^{-9} m\). The value of \(x\) is (Given. Young's modulus \(Y =2 \times 10^{11} Nm ^{-2}\) અને \(\left.g=10\, ms ^{-2}\right)\) 2022 Hard
61. 61. A wire of length \(L\) and radius \(r\) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(F\), its length increases by \(5\,cm\). Another wire of the same material of length \(4 L\) and radius \(4\,r\) is pulled by a force \(4\,F\) under same conditions. The increase in length of this wire is \(....cm\). 2022 Hard
62. 62. A wire of length \(L\) is hanging from a fixed support. The length changes to \(L _{1}\) and \(L _{2}\) when masses \(1 \,kg\) and \(2 \,kg\) are suspended respectively from its free end. Then the value of \(L\) is equal to .................. 2022 Hard
63. 63. If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will : 2022 Easy
64. 64. In an experiment to determine the Young's modulus, steel wires of five different lengths \((1,2,3,4\) and \(5\,m )\) but of same cross section \(\left(2\,mm ^{2}\right)\) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is \(x \times 10^{11}\,Nm ^{-2}\), then the value of \(x\) is
    2022 Hard
65. 65. The area of cross section of the rope used to lift a load by a crane is \(2.5 \times 10^{-4} m ^{2}\). The maximum lifting capacity of the crane is \(10\) metric tons. To increase the lifting capacity of the crane to \(25\) metric tons, the required area of cross section of the rope should be.\(.........\times 10^{-4} \,m ^{2}\) (take \(g =10\, ms ^{-2}\) ) 2022 Medium
66. 66. The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of \(5 \times 10^{-4}\) is \(\dots \; kJ / m ^{3}\). Assume that material is elastic upto the linear strain of \(5 \times 10^{-4}\).
    2022 Hard
67. 67. The elongation of a wire on the surface of the earth is \(10^{-4} \; m\). The same wire of same dimensions is elongated by \(6 \times 10^{-5} \; m\) on another planet. The acceleration due to gravity on the planet will be \(\dots \; ms ^{-2}\). (Take acceleration due to gravity on the surface of earth \(=10 \; m / s ^{-2}\) ) 2022 Hard
68. 68. The force required to stretch a wire of crosssection \(1 cm ^{2}\) to double its length will be ........ \( \times 10^{7}\,N\) (Given Yong's modulus of the wire \(=2 \times 10^{11}\,N / m ^{2}\) ) 2022 Hard
69. 69. A stone of mass \(20\, {g}\) is projected from a rubber catapult of length \(0.1\, {m}\) and area of cross section \(10^{-6} \,{m}^{2}\) stretched by an amount \(0.04\, {m}\). The velocity of the projected stone is \(....\,m\,/s.\) (Young's modulus of rubber \(=0.5 \times 10^{9}\, {N} / {m}^{2}\) ) 2021 Hard
70. 70. A uniform metallic wire is elongated by \(0.04\, m\) when subjected to a linear force \(F\). The elongation, if its length and diameter is doubled and subjected to the same force will be ..... \(cm .\) 2021 Hard
71. 71. Four identical hollow cylindrical columns of mild steel support a big structure of mass \(50 \times 10^{3} {kg}\), The inner and outer radii of each column are \(50\; {cm}\) and \(100 \;{cm}\) respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use \(\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]\) 2021 Medium
72. 72. If \(Y, K\) and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters. 2021 Medium
73. 73. The area of cross-section of a railway track is \(0.01\, {m}^{2}\). The temperature variation is \(10^{\circ} {C}\). Coefficient of linear expansion of material of track is \(10^{-5} /{ }^{\circ} {C}\). The energy stored per meter in the track is ...... \({J} / {m} .\) (Young's modulus of material of track is \(10^{11} \,{Nm}^{-2}\) )) 2021 Hard
74. 74. The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of increase in density of material, when a pressure \(P\) is applied uniformly on all sides, will be 2021 Medium
75. 75. Two blocks of masses \(3 \,{kg}\) and \(5\, {kg}\) are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \(\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}\). What is the minimum radius of the wire? (Take \(\left.g=10\, {ms}^{-2}\right)\) (in \(cm\))
    2021 Hard
76. 76. Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) is 2021 Hard
77. 77. Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are \(Y_{1}\) and \(Y_{2}\). The combination behaves as a single wire then its Young's modulus is: 2021 Medium
78. 78. Wires \({W}_{1}\) and \({W}_{2}\) are made of same material having the breaking stress of \(1.25 \times 10^{9} \,{N} / {m}^{2}\) \({W}_{1}\) and \({W}_{2}\) have cross-sectional area of \(8 \times 10^{-7}\, {m}^{2}\) and \(4 \times 10^{-7}\, {m}^{2}\), respectively. Masses of \(20 \,{kg}\) and \(10\, {kg}\) hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is \(.....{kg}\) (Use \(\left.{g}=10\, {m} / {s}^{2}\right)\)
    2021 Hard
79. 79. A body of mass \(\mathrm{m}=10\; \mathrm{kg}\) is attached to one end of a wire of length \(0.3\; \mathrm{m} .\) The maximum angular speed (in \(rad \;s^{-1}\) ) with which it can be rotated about its other end in space station is (Breaking stress of wire \(=4.8 \times 10^{7} \;\mathrm{Nm}^{-2}\) and area of cross-section of the wire \(=10^{-2}\; \mathrm{cm}^{2}\) ) is 2020 Hard
80. 80. A cube of metal is subjected to a hydrostatic pressure of \(4\;GPa.\) The percentage change in the length of the side of the cube is close to.......\(\%\)
    (Given bulk modulus of metal, \(B =8 \times 10^{10}\, Pa\) ) 2020 Medium
81. 81. Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is \(1: 4,\) the ratio of their diameters is 2020 Medium
82. 82. A boy’s catapult is made of rubber cord which is \(42\, cm\) long, with \(6\, mm\) diameter of cross -section and of negligible mass. The boy keeps a stone weighing \(0.02\, kg\) on it and stretches the cord by \(20\, cm\) by applying a constant force. When released, the stone flies off with a velocity of \(20\, ms^{-1}\). Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to 2019 Medium
83. 83. A rod of length \(L\) at room temperature and uniform area of cross section \(A\), is made of a metal having coefficient of linear expansion \(\alpha {/^o}C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by \(\Delta \,TK\). Young’s modulus, \(Y\), for this metal is 2019 Medium
84. 84. A steel wire having a radius of \(2.0\, mm\), carrying a load of \(4\, kg\), is hanging from a ceiling. Given that \(g = 3.1\pi \,m{s^{ - 2}}\) , what will be the tensile stress that would be developed in the wire? 2019 Medium
85. 85. In an experiment, brass and steel wires of length \(1\,m\) each with areas of cross section \(1\,mm^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of \(0.2\,mm\) is [Given, the Young’s Modulus for steel and brass are respectively \(120\times 10^9\,N/m^2\) and \(60\times 10^9\,N/m^2\) ] 2019 Medium
86. 86. The elastic limit of brass is \(379\,MPa.\) .......... \(mm\) should be the minimum diameter of a brass rod if it is to support a \(400\,N\) load without exceeding its elastic limit . 2019 Medium
87. 87. Young’s moduli of two wires \(A\) and \(B\) are in the ratio \(7 : 4\). Wire \(A\) is \(2\, m\) long and has radius \(R\). Wire \(A\) is \(2\, m\) long and has radius \(R\). Wire \(B\) is \(1.5\, m\) long and has radius \(2\, mm\). If the two wires stretch by the same length for a given load, then the value of \(R\) is close to ......... \(mm\) 2019 Medium
88. 88. A solid sphere of radius \(r\) made of a soft material of bulk modulus \(K\) is surrounded by a liquid in a cylindrical container. A massless piston of area \(a\) floats on the surface of the liquid, covering entire crosssection of cylindrical container. When a mass \(m\) is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \(\left( {\frac{{dr}}{r}} \right)\) is  2018 Medium
89. 89. As shown in the figure, forces of \(10^5\,N\) each are applied in opposite directions, on the upper and lower faces of a cube of side \(10\,cm\), shifting the upper face parallel to itself by \(0.5\,cm\) . If the side of another cube of the same material is, \(20\,cm\) then under similar conditions as above, the displacement will be......... \(cm\)
    2018 Easy
90. 90. A compressive force, \(F\) is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta T\). The net change in its length is zero. Let \(l\) be the length of the rod, \(A\) its area of cross- section, \(Y\) its Young's modulus, and \(\alpha \) its coefficient of linear expansion. Then, \(F\) is equal to 2017 Medium
91. 91. A man grows into a giant such that his linear dimensions increase by a factor of \(9\). Assuming that his density remains same, the stress in the leg will change by a factor of 2017 Hard
92. 92. A bottle has an opening of radius \(a\) and length \(b\). A cork of length band radius \(\left( {a + \Delta a} \right)\) where \(\left( {\Delta a <  < a} \right)\) is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is \(B\) and frictional coefficient between the bottle and cork is \(\mu \) then the force needed to push the cork into the bottle is
    2016 Medium
93. 93. A thin \(1 \,m\) long rod has a radius of \(5\, mm\). A force of \(50\,\pi kN\) is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is \(0.01\, mm\), which of the following statements is false ? 2016 Easy
94. 94. 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 \(R\) and \(3R,\)  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  2016 Hard
95. 95. In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is  2014 Medium
96. 96. Steel ruptures when a shear of \(3 .5 \times 10^8\,\,N\,m^{-2}\) is applied. The force needed to punch a \(1\,cm\) diameter hole in a steel sheet \(0.3\,cm\) thick is nearly 2014 Medium
97. 97. The bulk moduli of ethanol, mercury and water are given as \(0.9, 25\) and \(2 .2\) respectively in units of \(10^9\, Nm^{-2}\) . For a given value of pressure, the fractional compression in volume is \(\frac{{\Delta V}}{V}\). Which of the following statements about \(\frac{{\Delta V}}{V}\) for these three liquids is correct ? 2014 Medium
98. 98. A copper wire of length \(1.0\, m\) 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 \(1.0\times10^{11}\, Nm^{-2}\) and \(2.0\times10^{11}\, Nm^{- 2}\), the total extension of the composite wire is ........ \(mm\) 2013 Medium
99. 99. A uniform wire (Young's modulus \(2 \times 10^{11}\, Nm^{-2}\) ) is subjected to longitudinal tensile stress of \(5 \times 10^7\,Nm^{-2}\) . If the over all volume change in the wire is \(0.02\%,\) the fractional decrease in the radius of the wire is close to 2013 Medium
100. 100. 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
     2013 Hard

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