Elasticity (Stress-Strain & Moduli) — Practice Questions

Free NEET Physics multiple-choice questions on Elasticity (Stress-Strain & Moduli). Attempt each question and reveal the answer with a full explanation.

What is the work done in stretching a wire of length L and area of cross-section A to a strain ? 1 2 Y A L 2 Y A L 2 1 2 Y A L Y A L In a stress-strain graph, the material which has a large plastic range before fracture is called: Ductile Brittle Elastic Elastomer If is the coefficient of linear expansion and is the coefficient of volume expansion for an isotropic solid, then: = 3 = 2 = / 3 = A wire of length L and cross-sectional area A is stretched by a force F . If the Young's modulus is Y , the longitudinal strain is: F / (AY) F / A AY / F FL / (AY) In a stress-strain graph, the Young's Modulus can be determined from: The slope of the linear portion of the graph The area under the curve The value of stress at the fracture point The intercept on the Y-axis The energy stored per unit volume in a wire of Young's modulus Y and breaking stress S just before it breaks is: S 2 / 2Y S / 2Y S 2 / Y 2S 2 / Y Two rods of different materials, having coefficients of linear expansion 1, 2 and initial lengths L 1, L 2 respectively, are joined. The difference in their lengths remains constant at all temperatures if: L 1 1 = L 2 2 L 1 2 1 = L 2 2 2 L 1 2 = L 2 1 L 1 1 2 = L 2 2 2 Which of the following materials is most elastic? Steel Rubber Glass Copper The elastic energy density stored in a wire of Young's modulus Y when it is subjected to a longitudinal strain is given by: 1 2 Y 2 Y 2 1 2 Y 2 1 2 Y The potential energy of a stretched wire of length L and area A with extension l is U . If the same wire is stretched to an extension 2l , the new potential energy will be: 4U 2U U/2 8U A wire can support a maximum load of W . If the wire is cut into four equal parts, the maximum load that each part can support is: W W/4 2W 4W If the length of a wire is doubled and its radius is halved, then its Young's modulus will: Remain unchanged Become double Become eight times Become four times The breaking stress of a wire depends upon: Material of the wire Length of the wire Radius of the wire Shape of the cross-section The Young's modulus of the material of a wire is Y . If it is stretched by a stress S , the elastic energy stored per unit volume is: S 2 / 2Y Y S 2 / 2 S / 2Y S 2 Y / 2 The relation between Young's modulus Y , Bulk modulus B , and Poisson's ratio is given by: Y = 3B(1 - 2 ) Y = 2B(1 - 3 ) Y = 3B(1 + ) Y = 3B(1 - ) The stress-strain graphs for two materials A and B are shown in the figure. Young's modulus of material A is: Greater than B Less than B Equal to B Twice that of B The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied? Length = 50 cm, diameter = 0.5 mm Length = 100 cm, diameter = 1 mm Length = 200 cm, diameter = 2 mm Length = 300 cm, diameter = 3 mm When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+l) . The elastic potential energy stored in the extended wire is : 1 2 MgL Mgl MgL 1 2 Mgl A wire of length L , area of cross section A is hanging from a fixed support. The length of the wire changes to L 1 when mass M is suspended from its free end. The expression for Young’s modulus is : Mg(L 1-L) AL MgL AL 1 MgL A(L 1-L) MgL 1 AL Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is 2W/A W/A W/2A Zero Pumice stone is an example of Sol Gel Solid sol Foam The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus, respectively, are 8 10 8 N m -2 and 2 10 11 N m -2 , is: 4 mm 0.4 mm 40 mm 8 mm With the rise in temperature, the Young's modulus of a material generally: Decreases Increases Remains constant First increases then decreases A metallic bar of Young’s modulus, 0.5 10 11 N m -2 and coefficient of linear thermal expansion 10 -5 C -1 , length 1 m and area of cross-section 10 -3 m 2 is heated from 0 C to 100 C without expansion or bending. The compressive force developed in it is : 5 10 3 N 50 10 3 N 100 10 3 N 2 10 3 N The stress-strain curves are drawn for two different materials X and Y . It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y . We can say that materials X and Y are respectively: Brittle and Ductile Ductile and Brittle Brittle and Plastic Plastic and Ductile If the ratio of radii of two wires of same material is 2:1 and ratio of their lengths is 4:1 , then the ratio of the normal forces required to produce the same change in the length of these two wires is: 1:1 2:1 4:1 1:4 The Poisson's ratio of a material is 0.5 . If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4 % . The percentage increase in its length is: 4 % 2 % 1 % 8 % A copper rod of length 2 m is fixed between two rigid supports. If the temperature is increased by 50 C , find the thermal stress developed in the rod. ( Y = 1.2 10 11 N/m 2 , = 1.7 10 -5 / C ) 1.02 10 8 N/m 2 2.04 10 8 N/m 2 5.1 10 7 N/m 2 1.02 10 7 N/m 2 Two rods of different materials having coefficients of linear expansion 1 and 2 and Young's moduli Y 1 and Y 2 are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If 1 : 2 = 2 : 3 , the thermal stresses developed in the two rods are equal provided Y 1 : Y 2 is: 3:2 2:3 1:1 4:9 A steel wire is 1 m long and 1 mm 2 in area of cross-section. If it is stretched by 1 mm , the work done is ( Y = 2 10 11 N/m 2 ): 0.1 J 1.0 J 10 J 0.01 J For a material, the stress-strain graph is a straight line passing through origin up to stress of 10 8 N/m 2 . If the strain at this stress is 10 -3 , then the energy stored per unit volume of the material is: 5 10 4 J/m 3 10 5 J/m 3 2 10 5 J/m 3 5 10 5 J/m 3 For a given material, the Young's modulus is 2.4 times its modulus of rigidity. The Poisson's ratio of the material is: 0.2 0.5 0.3 0.4 A steel rod of length 1 m and cross-sectional area 1 cm 2 is heated from 0 ∘ C to 100 ∘ C without being allowed to expand or bend. What is the tension produced in the rod? ( Y = 2 10 11 N/m 2 , α = 1.2 10 -5 / ∘ C ) 2.4 10 4 N 1.2 10 4 N 2.4 10 5 N 1.2 10 5 N A wire of length L and radius r is fixed at one end and a force F is applied to the other end to produce an extension l . The work done in stretching the wire is: 1 2 Fl Fl 1 2 YlL Yl 2/L A copper wire and a steel wire of the same length and cross-section are joined end to end. The composite wire is stretched by a force F . The ratio of the elongation of the copper wire to the steel wire is: ( Y steel = 2 10 11 Pa , Y copper = 1.1 10 11 Pa ) 20:11 11:20 1:1 2:1 A heavy uniform rope of length L and mass M is hanging from a rigid support. The longitudinal stress in the rope at a distance x from the lower end is: Mgx / (AL) Mg(L-x) / (AL) MgL / (Ax) Mgx / A The theoretically possible values for Poisson's ratio for an isotropic elastic solid lie between: -1 and +0.5 -1 and +1 0 and +0.5 0.2 and 0.8 The phenomenon where the strain in a material lags behind the applied stress is known as: Elastic hysteresis Elastic fatigue Plasticity Yielding A metal rod is shaped into a ring with a small gap. When the ring is heated, the width of the gap: Increases Decreases Remains the same Initially increases then decreases If a wire is stretched such that its radius becomes 1/n times its original radius, while volume remains constant, the new resistance R' in terms of original resistance R is: n 4 R n 2 R n R n 8 R The relation between Young's modulus Y , bulk modulus B and modulus of rigidity is given by: Y = 9B 3B + Y = 3B 9B + Y = 9B B + 3 Y = 3B B + 3 A uniform wire of length L and mass M is suspended from the ceiling. If the Young's modulus of the wire is Y , the elongation of the wire due to its own weight is: MgL 2AY MgL AY 2MgL AY MgL 4AY If the interatomic force constant of a material is k and the interatomic distance is r 0 , the Young's modulus Y is given by: k/r 0 k r 0 k/r 0 2 k r 0 2 Torsional rigidity of a solid cylinder of length L , radius r and shear modulus is proportional to: r 4/L r 2/L r 4 L r/L 2 When a circular hole in a metal plate is heated, the diameter of the hole: Increases Decreases Remains unchanged Depends on the material 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 3A . If the length of wire 1 increases by x on applying force F , how much force is needed to stretch wire 2 by the same amount? 9F 4F 6F F A wire of length L and radius r is clamped at one end. On stretching the other end with a force F , the increase in length is l . If another wire of the same material but of length 2L and radius 2r is stretched with a force 2F , the increase in length will be: l l/2 2l 4l If the work done in stretching a wire by 1 mm is 2 J , the work done in stretching the same wire by another 1 mm is: 6 J 2 J 4 J 8 J A steel wire of length 4.7 m and cross-section 3.0 10 -5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-section 4.0 10 -5 m 2 under a given load. The ratio of the Young's modulus of steel to that of copper is: 1.79 1.52 1.91 1.33 The work done in stretching a wire of length L and area of cross-section A by an amount l is W . If another wire of the same material and same area of cross-section but of length 2L is stretched by the same amount l , the work done will be: W/2 W 2W 4W A wire of length L and radius r is fixed at one end and a force F is applied at the other end. The elongation is l . For another wire of the same material, length 2L and radius 2r , the same force F will produce an elongation of: l/2 l 2l 4l Two wires of the same length and material are stretched by the same force. If their radii are in the ratio 1:2 , then their elongations are in the ratio: 4 : 1 1 : 4 2 : 1 1 : 2 For a given material, the Young's modulus is Y and the modulus of rigidity is . If Y = 3 , then the Poisson's ratio is: 0.5 0.3 0.25 0 The stress-strain graphs for two materials A and B are shown in the figure. Material A has a higher slope in the elastic region and a longer region between the elastic limit and the fracture point compared to material B . Which of the following is true? A is more elastic and more ductile than B A is less elastic and more brittle than B B is more elastic and more ductile than A B is less elastic and more ductile than A A wire of length L and radius r is stretched by a load W . If the same load is applied to a wire of the same material but length 2L and radius 2r , the energy stored in the second wire as compared to the first wire is: Half Double Same One-fourth The Young's modulus of a perfectly rigid body is: Infinite Zero 1 A finite non-zero constant A steel wire is 4 m long and 2 mm in diameter. Young's modulus of steel is 2 10 11 Pa . If a force of 628 N is applied, the extension produced is (Take = 3.14 ): 4 10 -4 m 2 10 -4 m 8 10 -4 m 1 10 -4 m The Poisson's ratio for a material is 0.25 . If the longitudinal strain is 2 10 -3 , the fractional change in volume V / V is: 1 10 -3 2 10 -3 4 10 -3 0.5 10 -3 Copper of fixed volume 'V', is drawn into wire of length ' l '. When this wire is subjected to a constant force 'F', the extension produced in the wire is ' l '. Which of the following graphs is a straight line ? l versus 1 l l versus l 2 l versus 1 l 2 l versus l Which property of colloids is not dependent on the charge on colloidal particles ? Coagulation Electrophoresis Electro - osmosis Tyndall effect Lithium has a bcc structure. Its density is 530 kg m -3 and its atomic mass is 6.94 g mol -1 . Calculate the edge length of a unit cell of Lithium metal. (N A = 6.02 10 23 mol -1 ) 154 pm 352 pm 527 pm 264 pm The density of a metal at normal pressure is . Its density when it is subjected to an excess pressure p is ' . If B is Bulk modulus of the metal, the ratio of ' is 1+ B p 1 1- p B 1+ p B 1 1+ p B Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by l on applying a force F, how much force is needed to stretch the second wire by the same amount? 4 F 6 F 9 F F Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer from the options given below Both (A) and (R) are true and (R) is not the correct explanation of (A) (A) is true but (R) is false (A) is false but (R) is true Both (A) and (R) are true and (R) is the correct explanation of (A) Match List I with List II: array llll ; & List I & ; & List II A. & Young’s Modulus & I. & d L ( L d ) B. & Compressibility & II. & FL A( L) C. & Bulk Modulus & III. & - 1 P ( V V ) D. & Poisson’s Ratio & IV. & -P ( V V ) array Choose the correct answer from the options given below: A-III, B-II, C-I, D-IV A-II, B-III, C-IV, D-I A-I, B-IV, C-III, D-II A-IV, B-I, C-II, D-III Which of the following represents the relation between Young's Modulus ( Y ), Bulk Modulus ( B ) and Modulus of Rigidity ( )? 9/Y = 3/ + 1/B Y = (B + )/2 9/Y = 1/ + 3/B Y = 3B / (B + ) A steel wire is stretched by 1 kg load. If the radius of the wire is doubled, its Young's modulus will: Remain unchanged Become double Become half Become four times The potential energy U between two atoms in a diatomic molecule as a function of distance r is given by U(r) = a r 12 - b r 6 . The atoms are in stable equilibrium at a distance r 0 equal to: ( 2a b ) 1/6 ( a b ) 1/6 ( a 2b ) 1/6 ( 11a 5b ) 1/6 The ratio of the bulk modulus of an ideal gas at constant pressure (isobaric) to that at constant temperature (isothermal) is: 0 1 A copper wire of length 2.2 m and a steel wire of length 1.6 m , both of diameter 3.0 mm , are connected end to end. When stretched by a load, the net elongation is found to be 0.70 mm . The load applied is: ( Y steel = 2 10 11 N/m 2 , Y copper = 1.1 10 11 N/m 2 ) 1.8 10 2 N 1.2 10 2 N 2.4 10 2 N 3.0 10 2 N The value of Poisson's ratio for a material is 0.4 . If the longitudinal strain produced in a wire of this material is 0.05 , the percentage change in its volume is: 1 % 2 % 5 % 0.4 % The radius of a mountain on Earth is limited by the shear strength of the rock. If the density of the rock is and the maximum shear stress it can withstand is S , the maximum height h of the mountain is approximately: S / ( g) S / ( g) 2S / ( g) S 2 / ( g) A wire of length L is hanging from a fixed support. If it is stretched by a load Mg , the extension is l . The work done in stretching is 1/2 Mgl . This work done is stored in the wire as: Elastic potential energy Kinetic energy Thermal energy Gravitational potential energy The shear modulus (modulus of rigidity) for an ideal liquid is: Zero Infinite One Dependent on its density