Young's Modulus PYQs: JEE Mains Physics

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1. 1. A metal string \(A\) is suspended from a rigid support and its free end is attached to a block of mass \(M\). Second block having mass \(2M\) is suspended at the bottom of the first block using a string \(B\). The area of cross sections of strings \(A\) and \(B\) are same. The ratio of lengths of strings of \(A\) to \(B\) is \(2\) and the ratio of their Young's moduli \((Y_A/Y_B)\) is \(0.5\). The ratio of elongations in \(A\) to \(B\) is ______. 2026 Medium
2. 2. A string \(A\) of length \(0.314\) m and Young's modulus \(2 \times 10^{10}\) N/m\(^2\) is connected to another string \(B\) of length and Young's modulus both twice of those of \(A\). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \(0.8\) kg. The net change in length of the combination is _____ mm. (radius of both the strings is \(0.2\) mm and acceleration due to gravity \(= 10\) m/s\(^2\)) (Mass of both strings is to be neglected as compared to the mass of load) 2026 Hard
3. 3. Figure represents the extension (\(\Delta l\)) of a wire of length \(1\) meter, suspended from the ceiling of the room at one end with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}\) m\(^2\) then the Young's modulus of the wire is __________ N/m\(^2\).
   2026 Medium
4. 4. The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\). 2026 Easy
5. 5. The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?
   2026 Medium
6. 6. The two wires \(A\) and \(B\) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \(A\) and wire \(B\) is \(20/11\). When the joined wire is kept under certain tension the elongations in the wires \(A\) and \(B\) are equal. If the length of wire \(A\) is \(2.2\) m, then the length of wire \(B\) is _______ m. 2026 Medium
7. 7. The Young's modulus of steel wire of radius \(r\) and length \(L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\) 2026 Easy
8. 8. Two wires \(A\) and \(B\) made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections \(3.0 \times 10^{-5} m^2\) and \(4.5 \times 10^{-5} m^2\), respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of \(A\) to that of \(B\) is \(x : 3\). The value of x is ___________. 2026 Easy
9. 9. A 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 \(\mathrm{P} \times 10^{11} \mathrm{Nm}^{-2}\), where the value of P is: (Take \(\left.\mathrm{g}=3 \pi \mathrm{~m} / \mathrm{s}^2\right)\) 2025 Medium
10. 10. The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m. 2025 Easy
11. 11. Two wires A and B are made of same material having ratio of lengths \(\frac{L_A}{L_B}=\frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B}=2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations? 2025 Easy
12. 12. A wire of cross sectional area \(A\), modulus of elasticity \(2 \times 10^{11} \mathrm{Nm}^{-2}\) and length \(2 \mathrm{~m}\) is stretched between two vertical rigid supports. When a mass of \(2 \mathrm{~kg}\) is suspended at the middle it sags lower from its original position making angle \(\theta=\frac{1}{100}\) radian on the points of support. The value of \(A\) is _______ \(\times 10^{-4} \mathrm{~m}^2\) (consider \(\mathrm{x}<\mathrm{L}\) ). (given: \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )
    2024 Hard
13. 13. A wire of length \(L\) and radius \(r\) is clamped at one end. If its other end is pulled by a force \(F\), its length increases by \(l\). 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 _______. 2024 Hard
14. 14. Each of three blocks \(P\), \(Q\) and \(R\) shown in figure has a mass of \(3 \mathrm{~kg}\). Each of the wire \(A\) and \(B\) has cross-sectional area \(0.005 \mathrm{~cm}^2\) and Young's modulus \(2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Neglecting friction, the longitudinal strain on wire \(B\) is _______ \(\times 10^{-4}\). \(\left(\right.\) Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )
    2024 Hard
15. 15. One end of a metal wire is fixed to a ceiling and a load of \(2 \mathrm{~kg}\) hangs from the other end. A similar wire is attached to the bottom of the load and another load of \(1 \mathrm{~kg}\) 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 \(=0.005 \mathrm{~cm}^2\), \(\mathrm{Y}=2 \times 10^{11}\  \mathrm{Nm}^{-2}\) and \(\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]\) 2024 Hard
16. 16. Two metallic wires \(P\) and \(Q\) have same volume and are made up of same material. If their area of cross sections are in the ratio \(4: 1\) and force \(F_1\) is applied to \(\mathrm{P}\), an extension of \(\Delta l\) is produced. The force which is required to produce same extension in \(Q\) is \(\mathrm{F}_2\).The value of \(\frac{\mathrm{F}_1}{\mathrm{~F}_2}\) is _______. 2024 Hard
17. 17. Two persons pull a wire towards themselves. Each person exerts a force of \(200 \mathrm{~N}\) on the wire. Young's modulus of the material of wire is \(1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Original length of the wire is \(2 \mathrm{~m}\) and the area of cross section is \(2 \mathrm{~cm}^2\). The wire will extend in length by _______ \(\mu \mathrm{m}\). 2024 Hard
18. 18. With rise in temperature, the Young's modulus of elasticity _______. 2024 Hard
19. 19. Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______. 2024 Hard
20. 20. Young's modules of material of a wire of length '\(L\)' and cross-sectional area \(A\) is \(Y\). If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be _______. 2024 Hard
21. 21. A \(100\,m\) long wire having cross-sectional area \(6.25 \times 10^{-4}\,m ^2\) and Young's modulus is \(10^{10}\,Nm ^{-2}\) is subjected to a load of \(250\,N\), then the elongation in the wire will be : 2023 Easy
22. 22. A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections) 2023 Medium
23. 23. A steel rod has a radius of \(20\,mm\) and a length of \(2.0\,m\). A force of \(62.8\,kN\) stretches it along its length. Young's modulus of steel is \(2.0 \times 10^{11}\,N / m ^2\). The longitudinal strain produced in the wire is \(..........\times 10^{-5}\) 2023 Easy
24. 24. 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 \(l\). Another wire of same material of length \(2 L\) and radius \(2 r\) is pulled by a force \(2 f\). Then the increase in its length will be 2023 Medium
25. 25. As 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 \(45^{\circ}\) with the load axis. The length of wire is \(62.8\,cm\) and its diameter is \(4\,mm\). The Young's modulus is found to be \(x \times\) \(10^4\,Nm ^{-2}\). The value of \(x\) is
    2023 Easy
26. 26. 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
27. 27. 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
28. 28. 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
29. 29. 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
30. 30. 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
31. 31. 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
32. 32. 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
33. 33. 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
34. 34. 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
35. 35. 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
36. 36. 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
37. 37. 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
38. 38. 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
39. 39. 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
40. 40. 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
41. 41. 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
42. 42. 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
43. 43. 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
44. 44. 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
45. 45. 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
46. 46. 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
47. 47. 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
48. 48. 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
49. 49. 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
50. 50. 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

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