Physics · JEE Main, NEET

Mechanical Properties of Solids

118 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

78MCQ40Numerical16With diagram
Start with question 1 See it move: Elasticity: stress, strain and Young’s modulus
  1. 1A wire of length LL and radius rr is stretched by length ll under tension FF. A wire of same material of length 2L2L and radius 2r2r under tension 2F2F will be stretched by:JEE Main/MCQ/Medium
  2. 2Young's modulus of a perfectly rigid body is:NEET/MCQ/Medium
  3. 3A steel wire of length 2 m2\,\text{m} and area 2 mm22\,\text{mm}^2 is stretched by 1 mm1\,\text{mm}. Work done in stretching is (Y=2×1011 N/m2Y = 2 \times 10^{11}\,\text{N/m}^2):JEE Main/MCQ/Medium
  4. 4Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
    Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
    Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Elasticity
  5. 5Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
    Assertion (A) : Steel is used in the construction of buildings and bridges.
    Reason (R) : Steel is more elastic and its elastic limit is high.
    In the light of above statements, choose the most appropriate answer from the options given below    JEE Main/MCQ/Medium/Elasticity
  6. 6The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5×10−45\times {10}^{-4} is _____ kJm−3kJ{m}^{-3}. Assume that material is elastic upto the linear strain of 5×10−45\times {10}^{-4},
    JEE Main/Numerical/Medium/Elasticity/With diagram
  7. 7The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line
    JEE Main/MCQ/Medium/Elasticity/With diagram
  8. 8Figure represents the extension (Δl\Delta l) of a wire of length 11 meter, suspended from the ceiling of the room at one end with a load WW connected to the other end. If the cross-sectional area of the wire is 10−510^{-5} m2^2 then the Young's modulus of the wire is __________ N/m2^2.
    JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres/With diagram
  9. 9The two wires AA and BB of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire AA and wire BB is 20/1120/11. When the joined wire is kept under certain tension the elongations in the wires AA and BB are equal. If the length of wire AA is 2.22.2 m, then the length of wire BB is _______ m.JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  10. 10A lift of mass 16001600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4×1084 \times 10^8 N/m2^2 and its radius is 44 mm, then maximum acceleration the lift can take is _______ m/s2^2. (take g=10g = 10 m/s2^2 and π=3.14\pi = 3.14)JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  11. 11Two wires as shown in the figure below, made of steel and have breaking stress of 12×10812 \times 10^8 N/m2^2. Area of cross-section of upper wire is 0.0080.008 cm2^2 and of lower wire is 0.0040.004 cm2^2. The maximum mass that can be added to pan without breaking any wire is _____ kg.
    (take     g=10g = 10 m/s2^2)
    JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres/With diagram
  12. 12The Young's modulus of steel wire of radius rr and length LL is YY. If the radius rr and length LL of the wire are doubled then the value of YYJEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  13. 13A metal string AA is suspended from a rigid support and its free end is attached to a block of mass MM. Second block having mass 2M2M is suspended at the bottom of the first block using a string BB. The area of cross sections of strings AA and BB are same. The ratio of lengths of strings of AA to BB is 22 and the ratio of their Young's moduli (YA/YB)(Y_A/Y_B) is 0.50.5. The ratio of elongations in AA to BB is ______.JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  14. 14A string AA of length 0.3140.314 m and Young's modulus 2×10102 \times 10^{10} N/m2^2 is connected to another string BB of length and Young's modulus both twice of those of AA. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.80.8 kg. The net change in length of the combination is _____ mm. (radius of both the strings is 0.20.2 mm and acceleration due to gravity =10= 10 m/s2^2) (Mass of both strings is to be neglected as compared to the mass of load)JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  15. 15A uniform wire of length ll of weight ww is suspended from the roof with a weight of WW at the other end. The stress in the wire at l3\dfrac{l}{3} distance from the top is (WA+2γwA)\left(\dfrac{W}{A} + \dfrac{2}{\gamma}\dfrac{w}{A}\right), where, AA is the cross sectional area of the wire. The value of γ\gamma is _______.JEE Main/Numerical/Medium/Young’s Modulus and Breaking Stres
  16. 16The diameter of a wire measured by a screw gauge of least count 0.0010.001 cm is 0.080.08 cm. The length measured by a scale of least count 0.10.1 cm is 150150 cm. When a weight of 100100 N is applied to the wire, the extension in length is 0.50.5 cm, measured by a micrometer of least count 0.0010.001 cm. The error in the measured Young's modulus is α×109\alpha \times 10^9 N/m2^2. The value of α\alpha is _______.
    (Ignore the contribution of the load to Young's modulus error calculation)    JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  17. 17Two wires AA and BB made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0×10−5 m23.0 \times 10^{-5} \mathrm{~m}^{2} and 4.5×10−5 m24.5 \times 10^{-5} \mathrm{~m}^{2}, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of AA to that of BB is x:3x: 3. The value of xx is ____\_\_\_\_.JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres
  18. 18The strain-stress plot for materials A,B,CA, B, C and DD is shown in the figure. Which material has the largest Young's modulus ?
    JEE Main/MCQ/Medium/Young’s Modulus and Breaking Stres/With diagram
  19. 19Two persons pull a wire towards themselves. Each person exerts a force of 200 N200 \mathrm{~N} on the wire. Young's modulus of the material of wire is 1×1011 N m−21 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}. Original length of the wire is 2 m2 \mathrm{~m} and the area of cross section is 2 cm22 \mathrm{~cm}^2. The wire will extend in length by ______ μm\mu \mathrm{m}.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  20. 20A wire of cross sectional area A, modulus of elasticity 2×1011Nm−22 \times 10^{11} \mathrm{Nm}^{-2} and length 2 m2 \mathrm{~m} is stretched between two vertical rigid supports. When a mass of 2 kg2 \mathrm{~kg} is suspended at the middle it sags lower from its original position making angle θ=1100\theta=\frac{1}{100} radian on the points of support. The value of A\mathrm{A} is _______ ×10−4 m2\times 10^{-4} \mathrm{~m}^2 (consider x<<Lx\lt \lt \mathrm{L} ).
    (given :     g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  21. 21Match List-I with List-II :
    $\begin{array}{|c|c|c|c|}
    \hline & \text { List-I } & & \text { List-II } \\
    \hline \text { (A) } & \text { A force that restores an elastic body of unit area to its original state } & \text { (I) } & \text { Bulk modulus } \\
    \hline \text { (B) } & \text { Two equal and opposite forces parallel to opposite faces } & \text { (II) } & \text { Young's modulus } \\
    \hline \text { (C) } & \begin{array}{l}
    \text { Forces perpendicular everywhere to the surface per unit area } \\
    \text { same everywhere }
    \end{array} & \text { (III) } & \text { Stress } \\
    \hline \text { (D) } & \text { Two equal and opposite forces perpendicular to opposite faces } & \text { (IV) } & \text { Shear modulus } \\
    \hline
    \end{array}$
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  22. 22The density and breaking stress of a wire are 6×104 kg/m36 \times 10^4 \mathrm{~kg} / \mathrm{m}^3 and 1.2×108 N/m21.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2 respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is 13rd \frac{1}{3}^{\text {rd }} of the value on the surface of earth. The maximum length of the wire with breaking is _____ m (take, g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 ).JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  23. 23An elastic spring under tension of 3 N3 \mathrm{~N} has a length aa. Its length is bb under tension 2 N2 \mathrm{~N}. For its length (3a−2b)(3 a-2 b), the value of tension will be______N\mathrm{N}.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  24. 24One end of a metal wire is fixed to a ceiling and a load of 2kg2kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1kg1kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be
    [Area of cross section of wire     =0.005cm2,Y=2×1011Nm−2=0.005{cm}^{2},Y=2\times {10}^{11}N{m}^{-2} and g=10ms−2g=10m{s}^{-2}]    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  25. 25With rise in temperature, the Young's modulus of elasticityJEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  26. 26Two blocks of mass 2kg2kg and 4kg4kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0×10−5m4.0\times {10}^{-5}m and Young's modulus of the metal is 2.0×1011Nm−22.0\times {10}^{11}N{m}^{-2}. The longitudinal strain developed in the wire is 1απ\dfrac{1}{\alpha \pi }. The value of α\alpha is _____. [Use g=10ms−2g=10m{s}^{-2})JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  27. 27Each of three blocks P,QP,Q and RR shown in figure has a mass of 3kg3kg. Each of the wire AA and BB has cross-sectional area 0.005cm20.005{cm}^{2} and Young's modulus 2×1011Nm−22\times {10}^{11}N{m}^{-2}. Neglecting friction, the longitudinal strain on wire BB is _____ ×10−4\times {10}^{-4}. (Take g=10ms−2g=10m{s}^{-2})JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  28. 28Young's modules of material of a wire of length LL and cross-sectional area AA is Y.Y. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  29. 29Two metallic wires PP and QQ have same volume and are made up of same material. If their area of cross sections are in the ratio 4:14:1 and force F1{F}_{1} is applied to PP, an extension of ∆l∆l is produced. The force which is required to produce same extension in QQ is F2{F}_{2}. The value of F1F2\dfrac{{F}_{1}}{{F}_{2}} is ______.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  30. 30A wire of length LL and radius rr is clamped at one end. If its other end is pulled by a force FF, its length increases by ll. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  31. 31A wire of length LL and radius rr is clamped rigidly at one end. When the other end of the wire is pulled by a forceff, its length increases by ll. Another wire of same material of length 2L2L and radius 2r2r is pulled by a force 2f2f. Then the increase in its length will be:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  32. 32The length of a wire becomes l1{l}_{1} and l2{l}_{2} when 100N100N and 120N120N tension are applied respectively. If 10l2=11l110{l}_{2}=11{l}_{1}, then the natural length of wire will be 1xl1\dfrac{1}{x}{l}_{1}. Here the value of xx isJEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  33. 33Young’s moduli of the material of wires A and B are in the ratio of 1:41:4, while its area of cross sections are in the ratio of 1:31:3. 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]JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  34. 34Two wires each of radius 0.2cm0.2cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______10–6m{10}^{–6}m. [Young's modulus for steel =2×1011Nm–2=2\times {10}^{11}N{m}^{–2} and g=10ms–2g=10m{s}^{–2}]
    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  35. 35An aluminium rod with Young’s modulus Y=7.0×1010Nm−2Y=7.0\times {10}^{10}N{m}^{-2} undergoes elastic strain of 0.040.04%. The energy per unit volume stored in the rod in SISI unitJEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  36. 36A metal block of mass mm is suspended from a rigid support through a metal wire of diameter 14mm14mm. The tensile stress developed in the wire under equilibrium state is 7×105Nm–27\times {10}^{5}N{m}^{–2}. The value of mass mm is ______ kgkg.
    (Take     g=9.8ms−2g=9.8m{s}^{-2} and π=227\pi =\dfrac{22}{7})    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  37. 37A steel rod has a radius of 20mm20mm and a length of 2.0m.2.0m. A force of 62.8kN62.8kN stretches it along its length. Young's modulus of steel is 2.0×1011Nm−22.0\times {10}^{11}N{m}^{-2}. The longitudinal strain produced in the wire is _________\times {10}^{-5}.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  38. 38The Young's modulus of a steel wire of length 6m6m and cross-sectional area 3mm23{mm}^{2}, is 2×1111N/m22\times {11}^{11}N/{m}^{2} . The wire is suspended from its support on a given planet. A block of mass 4kg4kg is attached to the free end of the wire. The acceleration due to gravity on the planet is 14\dfrac{1}{4} of its value on the earth. The elongation of wire is (Take gg on the earth =10m/s2=10m/{s}^{2} ):JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  39. 39Under the same load, wire A having length 5.0m5.0m and cross section 2.5×10−5m22.5\times {10}^{-5}{m}^{2} stretches uniformly by the same amount as another wire BB of length 6.0m6.0m and a cross section of 3.0×10−5m23.0\times {10}^{-5}{m}^{2} stretches. The ratio of the Young's modulus of wire AA to that of wire BB will be:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  40. 40A force is applied to a steel wire AA, rigidly clamped at one end. As a result elongation in the wire is 0.2mm0.2mm. If same force is applied to another steel wire BB of double the length and a diameter 2.42.4 times that of the wire AA, the elongation in the wire BB will be (wires having uniform circular cross sections)JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  41. 41As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45∘45^{\circ} with the load axis. The length of wire is 62.8cm62.8cm and its diameter is 4mm4mm. The Young's modulus is found to be x×104Nm−2x\times {10}^{4}N{m}^{-2}
    The value of     xx is _______.
    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  42. 42A 100m100m long wire having cross-sectional area 6.25×10−4m26.25\times {10}^{-4}{m}^{2} and Young's modulus is 1010Nm−2{10}^{10}N{m}^{-2} is subjected to a load of 250N250N, then the elongation in the wire will be :JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  43. 43A metal wire of length 0.5m0.5m and cross-sectional area 10−4m2{10}^{-4}{m}^{2} has breaking stress 5×108Nm−25\times {10}^{8}N{m}^{-2}. A block of 10kg10kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms−1m{s}^{-1}.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  44. 44If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  45. 45A string of area of cross-section 4mm24{mm}^{2} and length 0.50.5 is connected with a rigid body of mass 2kg2kg. The body is rotated in a vertical circular path of radius 0.5m0.5m. The body acquires a speed of 5ms−15m{s}^{-1} at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ ×10−5\times {10}^{-5}. (Use Young's modulus 1011Nm−2{10}^{11}N{m}^{-2} and g=10ms−2g=10m{s}^{-2})JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  46. 46The force required to stretch a wire of cross-section 1cm21{cm}^{2} to double its length will be :
    (Given Yong's modulus of the wire     =2×1011Nm−2=2\times {10}^{11}N{m}^{-2})    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  47. 47In an experiment to determine the Young's modulus, steel wires of five different lengths (1,2,3,41,2,3,4 and 55) but of same cross-section (2mm2)\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×1011Nm−2x\times {10}^{11}N{m}^{-2}, then the value of xx is _____ .
    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  48. 48A steel wire of length 3.2m(YS=2.0×1011Nm−2)3.2m\left({Y}_{S}=2.0\times {10}^{11}N{m}^{-2}\right) and a copper wire of length 4.4m(YC=1.1×1011Nm−2)4.4m\left({Y}_{C}=1.1\times {10}^{11}N{m}^{-2}\right) , both of radius 1.4mm1.4mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4mm1.4mm. The load applied, in Newton, will be: (Given π=227\pi =\dfrac{22}{7})JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  49. 49A uniform heavy rod of mass 20kg20kg. Cross sectional area 0.4m20.4{m}^{2} and length 20m20m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x×10−9mx\times {10}^{-9}m. The value of xx is _____ .
    (Given. Young's modulus     Y=2×1011Nm−2Y=2\times {10}^{11}{Nm}^{-2} and g=10ms−2g=10m{s}^{-2} )    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  50. 50The area of cross section of the rope used to lift a load by a crane is 2.5×10−4m22.5\times {10}^{-4}{m}^{2}. The maximum lifting capacity of the crane is 1010 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
    (take     g=10ms−2g=10{ms}^{-2})    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  51. 51A wire of length LL and radius rr is clamped rigidly at one end. When the other end of the wire is pulled by a force FF, its length increases by 5cm5cm. Another wire of the same material of length 4L4L and radius 4r4r is pulled by a force 4F4F under same conditions. The increase in length of this wire is _____ cmcm.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  52. 52A wire of length LL is hanging from a fixed support. The length changes to L1{L}_{1} and L2{L}_{2} when masses 1kg1kg and 2kg2kg are suspended respectively from its free end. Then the value of LL is equal toJEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  53. 53Four identical hollow cylindrical columns of mild steel support a big structure of mass 50×103kg.50\times {10}^{3}kg. The inner and outer radii of each column are 50cm50cm and 100cm100cm respectively. Assuming uniform local distribution, calculate the compression strain of each column.
    [use     Y=2.0×1011Pa,g=9.8ms−2Y=2.0\times {10}^{11}Pa,g=9.8m{s}^{-2}]    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  54. 54A uniform heavy rod of weight 10kgms−2,10kg{ms}^{-2}, cross-sectional area 100cm2100{cm}^{2} and length 20cm20cm is hanging from a fixed support. Young modulus of the material of the rod is 2×1011Nm−2.2\times {10}^{11}N{m}^{-2}. Neglecting the lateral contraction, find the elongation of rod due to its own weight:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  55. 55Wires W1{W}_{1} and W2{W}_{2} are made of same material having the breaking stress of 1.25×109Nm−2.W11.25\times {10}^{9}N{m}^{-2}.{W}_{1} and W2{W}_{2} have cross-sectional area of 8×10−7m28\times {10}^{-7}{m}^{2} and 4×10−7m24\times {10}^{-7}{m}^{2}, respectively. Masses of 20kg20kg and 10kg10kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _____kgkg (Use g=10ms−2)\left.g=10m{s}^{-2}\right)
    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres/With diagram
  56. 56Two blocks of masses 3kg3kg and 5kg5kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is 24π×102Nm−2\dfrac{24}{\pi }\times {10}^{2}N{m}^{-2}. What is the minimum radius of the wire ?
    ( take     g=10ms−2)\left.g=10{ms}^{-2}\right)
    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres/With diagram
  57. 57Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y1{Y}_{1} and Y2{Y}_{2}. The combination behaves as a single wire then its Young's modulus is:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  58. 58The length of a metal wire is ℓ1,{\ell }_{1}, when the tension in it is T1{T}_{1} and is ℓ2{\ell }_{2} when the tension is T2.{T}_{2}. The natural length of the wire is:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  59. 59The value of tension in a long thin metal wire has been changed from T1{T}_{1} to T2{T}_{2}. The lengths of the metal wire at two different values of tension T1{T}_{1} and T2{T}_{2} are ℓ1{\ell }_{1} and ℓ2{\ell }_{2}, respectively. The actual length of the metal wire is:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  60. 60Two separate wires AA and BB are stretched by 2mm2mm and 4mm4mm respectively, when they are subjected to a force of 2N.2N. Assume that both the wires are made up of same material and the radius of wire BB is 44 times that of the radius of wire A.A. The length of the wires AA and BB are in the ratio of a:b.a:b. Then ab\dfrac{a}{b} can be expressed as 1x\dfrac{1}{x}, where xx is _____.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  61. 61The length of metallic wire is l1{l}_{1} when tension in it is T1{T}_{1}. It is l2{l}_{2} when the tension is T2{T}_{2}. The original length of the wire will be :JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  62. 62A uniform metallic wire is elongated by 0.04m0.04m when subjected to a linear force F.F. The elongation, if its length and diameter is doubled and subjected to the same force will be _________ cm.cm.JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  63. 63If Y,KY,K and η\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.JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  64. 64A wire of density 9×10–3kgcm–39\times {10}^{–3}kg{cm}^{–3} is stretched between two clamps 1m1m apart. The resulting strain in the wire is 4.9×10–44.9\times {10}^{–4}. The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire Y=9×1010Nm–2Y=9\times {10}^{10}{Nm}^{–2} ), (to the nearest integer),_______JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  65. 65A body of mass m=10kgm=10kg is attached to one end of a wire of length 0.3m0.3m. What is the maximum angular speed (in rads−1rad{s}^{-1}) with which it can be rotated about its other end in a space station without breaking the wire?
    [Breaking stress of wire     (σ)\left(\sigma \right)=4.8×107Nm−2=4.8\times {10}^{7}N{m}^{-2} and area of cross-section of the wire=10−2cm2={10}^{-2}c{m}^{2}]    JEE Main/Numerical/Medium/Young's Modulus and Breaking Stres
  66. 66Speed of a transverse wave on a straight wire (mass 6.0g,6.0g, length 60cm60cm and area of cross-section 1.0mm21.0m{m}^{2} is 90ms−190{ms}^{-1}. If the Young's modulus of wire is 16×1011Nm−216\times {10}^{11}N{m}^{-2}, the extension of wire over its natural length is:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  67. 67In an experiment, brass and steel wires of length 1m1m each with areas of cross section 1mm21m{m}^{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 required to produce a net elongation of 0.2mm0.2mm is,
    [Given, the Young's Modulus for steel and brass are, respectively,     120×109N/m2120\times {10}^{9}N/{m}^{2} and 60×109N/m260\times {10}^{9}N/{m}^{2} ]    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  68. 68The elastic limit of brass is 379MPa379MPa. The minimum diameter of a brass rod if it is to support a 400N400N load without exceeding its elastic limit will beJEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  69. 69Young's moduli of two wires AA and BB are in the ratio 7:47:4 . Wire AA is 2m2m long and has radius R.R. Wire BB is 1.5m1.5m long and has radius 2mm.2mm. If the two wires stretch by the same length for a given load, the value of RR is close to:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  70. 70A steel wire having a radius of 2.0mm2.0mm , carrying a load of 4kg,4kg, is hanging from a ceiling. Given that g=3.1πms−2,g=3.1\pi m{s}^{-2}, what will be the tensile stress that would be developed in the wire?JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  71. 71A boy’s catapult is made of rubber cord which is 42cm42cm long, with 6mm6mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg0.02kg on it and stretches the cord by 20cm20cm by applying a constant force. When released, the stone flies off with a velocity of 20ms−120m{s}^{-1} . Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  72. 72A rod, of length LL at room temperature and uniform area of cross section A,A, is made of a metal having coefficient of linear expansion α/∘C\alpha /^{\circ}C It is observed that an external compressive force FF is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by ∆TK∆TK Young's modulus, YY for this metal is:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  73. 73A man grows into a giant such that his linear dimensions increase by a factor of 9.9. Assuming that his density remains same, the stress in the leg will change by a factor of:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  74. 74A uniformly tapering conical wire is made from a material of Young's modulus YY and has a normal, unextended length LL. The radii, at the upper and lower ends of this conical wire, have values RR and 3R3R, respectively. The upper end of the wire is fixed to a rigid support and a mass MM is suspended from its lower end. The equilibrium extended length, of this wire, would equal:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  75. 75A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM{T}_{M} . If the Young's modulus of the material of the wire is YY, then 1Y\dfrac{1}{Y} is equal to:
    (    g=g=gravitational acceleration)    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  76. 76In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  77. 77Two blocks of masses m\mathrm{m} and M\mathrm{M} are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If M=2 m\mathrm{M}=2 \mathrm{~m}, then the stress produced in the wire is:
    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres/With diagram
  78. 78A copper wire of length 1.0 m1.0 \mathrm{~m} and a steel wire of length 0.5 m0.5 \mathrm{~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 mm1 \mathrm{~mm}. If the Young's modulii of copper and steel are respectively 1.0×10111.0 \times 10^{11} Nm−2\mathrm{Nm}^{-2} and 2.0×1011Nm−22.0 \times 10^{11} \mathrm{Nm}^{-2}, the total extension of the composite wire is :JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  79. 79A uniform wire (Young's modulus 2×1011Nm−22 \times 10^{11} \mathrm{Nm}^{-2} ) is subjected to longitudinal tensile stress of 5×107Nm−25 \times 10^7 \mathrm{Nm}^{-2}. If the overall volume change in the wire is 0.02%0.02 \%, the fractional decrease in the radius of the wire is close to:JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  80. 80If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are a,ba, b and cc respectively, then the corresponding ratio of increase in their lengths is :
    JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres/With diagram
  81. 81A steel wire can sustain 100 kg100 \mathrm{~kg} weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight ofJEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  82. 82A structural steel rod has a radius of 10 mm10 \mathrm{~mm} and length of 1.0 m1.0 \mathrm{~m}. A 100kN100 \mathrm{kN} force stretches it along its length. Young's modulus of structural steel is 2×1011Nm−22 \times 10^{11} \mathrm{Nm}^{-2}. The percentage strain is aboutJEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  83. 83Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area AA and wire-2 has cross-sectional area 3A3 A. If the length of wire 1 increases by Δx\Delta x on applying force FF, how much force is needed to stretch wire 2 by the same amount?JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  84. 84A wire elongates by ℓmm\ell \mathrm{mm} when a load W\mathrm{W} is hanged from it. If the wire goes over a pulley and two weights W\mathrm{W} each are hung at the two ends, the elongation of the wire will be (in mm\mathrm{mm} )JEE Main/MCQ/Medium/Young's Modulus and Breaking Stres
  85. 85The increase in the pressure required to decrease the volume (ΔV)(\Delta V) of water is 6.3×1076.3 \times 10^7 N/m2^2. The percentage decrease in the volume is _____. (Bulk modulus of water =2.1×109= 2.1 \times 10^9 N/m2^2.)JEE Main/MCQ/Medium/Bulk Modulus
  86. 86A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm30.8 \mathrm{~cm}^3. If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre. (\left(\right. Take 1 atm=105 Pa)\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)JEE Main/Numerical/Medium/Bulk Modulus
  87. 87The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is
    ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).    JEE Main/MCQ/Medium/Bulk Modulus
  88. 88The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7×106 Pa7 \times 10^6 \mathrm{~Pa}, would be ____ mm3\mathrm{mm}^3.
    (Given bulk modulus of copper     =1.4×1011 N m−2=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} )    JEE Main/Numerical/Medium/Bulk Modulus
  89. 89The increase in pressure required to decrease the volume of a water sample by 0.2%0.2 \% is P×105Nm−2\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}. Bulk modulus of water is 2.15×109Nm−22.15 \times 10^9 \mathrm{Nm}^{-2}. The value of P is ……\ldots\ldotsJEE Main/Numerical/Medium/Bulk Modulus
  90. 90The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.020.02% is _____ mm.
    (Take density of sea water     =103kgm−3={10}^{3}kg{m}^{-3}, Bulk modulus of rubber =9×108Nm−2=9\times {10}^{8}N{m}^{-2}, and g=10ms−2g=10m{s}^{-2})    JEE Main/Numerical/Medium/Bulk Modulus
  91. 91If average depth of an ocean is 4000m4000m and the bulk modulus of water is 2×109Nm−22\times {10}^{9}N{m}^{-2}, then fractional compression ΔVV\dfrac{\Delta V}{V} of water at the bottom of ocean is α×10−2\alpha \times {10}^{-2}. The value of α\alpha is _______, (Given, g=10ms−2,ρ=1000kgm−3g=10m{s}^{-2},\rho =1000kg{m}^{-3})JEE Main/Numerical/Medium/Bulk Modulus
  92. 92Under isothermal condition, the pressure of a gas is given by P=aV–3,P=a{V}^{–3}, where aa is a constant and VV is the volume of the gas. The bulk modulus at constant temperature is equal toJEE Main/MCQ/Medium/Bulk Modulus
  93. 93A certain pressure 'PP' is applied to 11 litre of water and 22 litre of a liquid separately. Water gets compressed to 0.010.01% whereas the liquid gets compressed to 0.030.03%. The ratio of Bulk modulus of water to that of the liquid is 3x\dfrac{3}{x}. The value of xx is ______.JEE Main/Numerical/Medium/Bulk Modulus
  94. 94Choose the correct relationship between Poisson ratio (σ)\left(\sigma \right), bulk modulus (K)(K) and modulus of rigidity (η)\left(\eta \right) of a given solid object:JEE Main/MCQ/Medium/Bulk Modulus
  95. 95The bulk modulus of a liquid is 3×1010Nm−23\times {10}^{10}{Nm}^{-2}. The pressure required to reduce the volume of liquid by 22% is :JEE Main/MCQ/Medium/Bulk Modulus
  96. 96When a rubber ball is taken to a depth of _______ mm in deep sea, its volume decreases by 0.50.5%
    (The bulk modulus of rubber     =9.8×108Nm−2=9.8\times {10}^{8}N{m}^{-2} Density of sea water =103kgm−3={10}^{3}kg{m}^{-3},g=9.8ms−2g=9.8m{s}^{-2})    JEE Main/Numerical/Medium/Bulk Modulus
  97. 97An object is located at 2km2km beneath the surface of the water. If the fractional compression ΔVV\dfrac{\Delta V}{V} is 1.361.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ______[Given: density of water is 1000kgm−31000kg{m}^{-3} and g=9.8ms−2.g=9.8{ms}^{-2}.JEE Main/MCQ/Medium/Bulk Modulus
  98. 98The normal density of a material is ρ\rho and its bulk modulus of elasticity is KK. The magnitude of increase in density of material, when a pressure PP is applied uniformly on all sides, will be :JEE Main/MCQ/Medium/Bulk Modulus
  99. 99A cube of metal is subjected to a hydrostatic pressure 4GPa4GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B=8×1010PaB=8\times {10}^{10}Pa)JEE Main/MCQ/Medium/Bulk Modulus
  100. 100A 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 aa floats on the surface of the liquid, covering entire cross-section 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 (drr)\left(\dfrac{dr}{r}\right) , is:JEE Main/MCQ/Medium/Bulk Modulus
  101. 101A bottle has an opening of radius aa and length bb. A cork of length bb and radius (a+∆a)\left(a+∆a\right) where (∆a≪a)\left(∆a≪a\right), is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is BB and the coefficient of friction between the bottle and cork is μ\mu, then the force needed to push the cork into the bottle is

    JEE Main/MCQ/Medium/Bulk Modulus/With diagram
  102. 102The bulk moduli of ethanol, mercury and water are given as 0.9,250.9,25 and 2.22.2 respectively in units of 109Nm−210^9 \mathrm{Nm}^{-2}. For a given value of pressure, the fractional compression in volume is ΔVV\frac{\Delta \mathrm{V}}{\mathrm{V}}. Which of the following statements about ΔVV\frac{\Delta V}{V} for these three liquids is correct ?JEE Main/MCQ/Medium/Bulk Modulus
  103. 103A cube has side length 55 cm and modulus of rigidity 10510^5 N/m2^2. The displacement produced by a force of 1010 N in the upper face of cube is _____ mm.JEE Main/Numerical/Medium/Shearing stress
  104. 104A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 105 N10^5 \mathrm{~N} at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement θ\theta of the rod axis from its original position would be : (shear moduli, G=1010 N/m2)\left.\mathrm{G}=10^{10} \mathrm{~N} / \mathrm{m}^2\right)JEE Main/MCQ/Medium/Shearing stress
  105. 105Two slabs with square cross section of different materials (1,2)(1,2) with equal sides (l)(l) and thickness d1\mathrm{d}_1 and d2\mathrm{d}_2 such that d2=2 d1\mathrm{d}_2=2 \mathrm{~d}_1 and l>d2l \gt \mathrm{d}_2. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is θ2=2θ1\theta_2=2 \theta_1. If the shear moduli of material 1 is 4×109 N/m24 \times 10^9 \mathrm{~N} / \mathrm{m}^2, then shear moduli of material 2 is x×109 N/m2\mathrm{x} \times 10^9 \mathrm{~N} / \mathrm{m}^2, where value of xx is ________.JEE Main/Numerical/Medium/Shearing stress
  106. 106A square aluminium (shear modulus is 25×109Nm−225\times {10}^{9}{Nm}^{-2}) slab of side 60cm60cm and thickness 15cm15cm is subjected to a shearing force (on its narrow face) of 18.0×104N18.0\times {10}^{4}N. The lower edge is riveted to the floor. The displacement of the upper edge is _____ μm\mu m.JEE Main/Numerical/Medium/Shearing stress
  107. 107The velocity of water in a river is 18kmh−118km{h}^{-1} near the surface. If the river is 5m5m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water=10−2poise={10}^{-2}poise.JEE Main/MCQ/Medium/Shearing stress
  108. 108Steel ruptures when a shear of 3.5×108 N m−23.5 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2} is applied. The force needed to punch a 1 cm1 \mathrm{~cm} diameter hole in a steel sheet 0.3 cm0.3 \mathrm{~cm} thick is nearly:JEE Main/MCQ/Medium/Shearing stress
  109. 109A copper wire of length 3 m3\text{ m} is stretched by 3 mm3\text{ mm} by applying an external force. The volume of the wire is 600×10−6 m3600 \times 10^{-6}\text{ m}^3. The elastic potential energy stored in the wire in stretched condition would be _______ J.
    (Given Young modulus of copper     =1.1×1011 N/m2= 1.1 \times 10^{11}\text{ N/m}^2)    JEE Main/Numerical/Medium/Work Done in Stretching a Wire
  110. 110A steel wire of length 2 m and Young's modulus 2.0×1011Nm−22.0 \times 10^{11} \mathrm{Nm}^{-2} is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and 10−310^{-3} respectively, then the elastic potential energy density of the wire is _______ ×105\times 10^5 (in SI units)JEE Main/Numerical/Medium/Work Done in Stretching a Wire
  111. 111The elastic potential energy stored in a steel wire of length 20m20m stretched through 2cm2cm is 80J.80J. The cross sectional area of the wire is _____ mm2.{mm}^{2}. (Given, Y=2.0×1011Nm–2Y=2.0\times {10}^{11}N{m}^{–2})JEE Main/Numerical/Medium/Work Done in Stretching a Wire
  112. 112A stone of mass 20g20g is projected from a rubber catapult of length 0.1m0.1m and area of cross section 10−6m2{10}^{-6}{m}^{2} stretched by an amount 0.04m.0.04m. The velocity of the projected stone is ms−1.m{s}^{-1}. (Young's modulus of rubber =0.5×109Nm−2=0.5\times {10}^{9}N{m}^{-2})JEE Main/Numerical/Medium/Work Done in Stretching a Wire
  113. 113The area of cross-section of a railway track is 0.01m2.0.01{m}^{2}. The temperature variation is 10∘C.10^{\circ}C. Coefficient of linear expansion of material of track is 10−5C−1∘.{10}^{-5}C-1^{\circ}. The energy stored per meter in the track is Jm−1.J{m}^{-1}. (Young's modulus of material of track is 1011Nm−2{10}^{11}N{m}^{-2})JEE Main/Numerical/Medium/Work Done in Stretching a Wire
  114. 114Two 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 1:4,1:4, the ratio of their diameters is:JEE Main/MCQ/Medium/Work Done in Stretching a Wire
  115. 115If SS is stress and YY is Young's modulus of material of a wire, the energy stored in the wire per unit volume isJEE Main/MCQ/Medium/Work Done in Stretching a Wire
  116. 116A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N200 \mathrm{~N} to the lower end. The weight stretches the wire by 1 mm1 \mathrm{~mm}. Then the elastic energy stored in the wire isJEE Main/MCQ/Medium/Work Done in Stretching a Wire
  117. 117A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is P×1011Nm−2\mathrm{P} \times 10^{11} \mathrm{Nm}^{-2}, where the value of P is: (Take g=3π m/s2)\left.\mathrm{g}=3 \pi \mathrm{~m} / \mathrm{s}^2\right)JEE Main/MCQ/Medium/Young's Modulus and Breaking Stress
  118. 118Two wires A and B are made of same material having ratio of lengths LALB=13\frac{L_A}{L_B}=\frac{1}{3} and their diameters ratio dAdB=2\frac{d_A}{d_B}=2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?JEE Main/MCQ/Medium/Young's Modulus and Breaking Stress

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