Mechanical Properties of Solids PYQs Set 2 (PDF)

Set 2 of 6 · Questions 31-60 of 156

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Mere Teacher · Previous Year Questions JEE Main Physics · Mechanical Properties of Solids · Set 2 (Q31-60)
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31. $A 100 m long wire having cross-sectional area 6.25 x 1 0^{- 4} m^{2} and Young's modulus is 1 0^{10} N m^{- 2} is subjected to a load of 250 N, then the elongation in the wire will be:$ (1) $6.25x 1 0^{- 3} m$ (2) $4x 1 0^{- 4} m$ (3) $6.25 x 1 0^{- 6} m$ (4) $4 x 1 0^{- 3} m$ 32. $A metallic rod breaks when strain produced is 0.2 % . The Young's modulus of the material of the rod is 7 \times 10^{9} N / m^{2} . The area of cross section to support a load of 10^{4} N is$ (1) $7.1 \times 10^{- 4} m^{2}$ (2) $7.1 \times 10^{- 8} m^{2}$ (3) $7.1 \times 10^{- 2} m^{2}$ (4) $7.1 \times 10^{- 6} m^{2}$ 33. $Let a steel bar of length l, breadth b and depth d be loaded at the centre by a load W . Then the sag or bending of beam is (Y = Young's modulus of material of steel)$ (1) $\frac{W l ^{3}}{2 b d ^{3} Y}$ (2) $\frac{W l ^{3}}{4 b d ^{3} Y}$ (3) $\frac{W l ^{2}}{2 b d ^{3} Y}$ (4) $\frac{W l ^{3}}{4 b d ^{2} Y}$ 34. $A steel rod of radius 20 mm and length of 2 m is acted upon by a force of 400 kN along the length. The values of stress and strain are respectively (Y_{steel} = 2 \times 10^{11} Nm^{- 2})$ (1) $1.96 \times 10^{8} Nm^{- 2}, 0.16 %$ (2) $3.18 \times 10^{8} Nm^{- 2}, 0.16 %$ (3) $3.18 \times 10^{8} Nm^{- 2}, 0.32 %$ (4) $4 \times 10^{8} Nm^{- 2}, 0.2 %$ 35. $The average depth of an oil well is . If the bulk modulus of oil is and the density of oil is . The fractional compression at the bottom of the well is (take, )$ (1) $3.75 %$ (2) $1.75 %$ (3) $2.75 %$ (4) $4.75 %$ 36. $Which of the following statement is incorrect?$ (1) $The bulk modulus for solids is much larger than for liquids.$ (2) $Gases are least compressible.$ (3) $The incompressibility of the solids is due to the tight coupling between neighbouring atoms.$ (4) $The reciprocal of the bulk modulus is called compressibility.$ 37. $The fractional compression of water at the depth of 2.5 km below the sea level is .Given, the Bulk modulus of water , density of water , acceleration due to gravity .$ (1) $1.25$ (2) $1.0$ (3) $1.75$ (4) $1.5$ 38. $The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?$ (1) $length = 100 cm, diameter = 1 mm$ (2) $length = 200 cm, diameter = 2 mm$ (3) $length = 300 cm, diameter = 3 mm$ (4) $length = 50 cm, diameter = 0.5 mm$ 39. $The increase in energy of a metal bar of length ' L' and cross-sectional area ' A' when compressed with a load ' M' along its length is (Y = Young's modulus of the material of metal bar)$ (1) $\frac{FL}{2 AY}$ (2) $\frac{F ^{2} L}{2 AY}$ (3) $\frac{FL}{AY}$ (4) $\frac{F ^{2} L ^{2}}{2 AY}$ 40. $The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is$ (1) $length 0.5 m, diameter 0.5 mm .$ (2) $length 1 m, diameter 1 mm .$ (3) $length 2 m, diameter 2 mm .$ (4) $length 3 m, diameter 3 mm .$ 41. $A copper wire and an aluminium wire have lengths in the ratio 5 : 2, diameters in the ratio 4 : 3 and forces applied in the ratio 4 : 5 . Find the ratio of increase in length of the copper wire to that aluminium wire. (Let Y_{Cu} = 1.1 \times 10^{11} Nm^{- 2}, Y_{Al} = 0.7 \times 10^{11} Nm^{- 2})$ (1) $\frac{176}{63}$ (2) $\frac{63}{88}$ (3) $\frac{189}{11}$ (4) $\frac{33}{89}$ 42. $A lift of mass m is connected to rope which is moving upward with maximum acceleration a . For maximum safe stress, the elastic limit of the rope is T . The minimum diameter of the rope is (g = gravitational acceleration)$ (1) $(\frac{2 m ( g + a )}{πT})^{1/2}$ (2) $(\frac{4 m ( g + a )}{πT})^{1/2}$ (3) $(\frac{( g + a )}{πT})^{1/2}$ (4) $(\frac{m ( g + a )}{2 πT})^{1/2}$ 43. $Copper of fixed volume 'V' is drawn into wire of length 'λ'. When this wire is subjected to a constant force 'F', the extension produced in the wire is 'Δλ'. Which of the following graph is a straight line?$ (1) $Δλ versus 1/λ$ (2) $Δλ versus λ2$ (3) $Δλ versus 1/λ2$ (4) $Δλ versus λ$ 44. $A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 \times 1 0^{3} kg/ m^{3} and 2.2 \times 1 0^{11} N/ m^{2} respectively?$ (1) $188.5 Hz$ (2) $178.2 Hz$ (3) $200.5 Hz$ (4) $770 Hz$ 45. $A stretched wire of a material whose Young's modulus Y = 2 \times 10^{11} N m^{- 2} has Poisson's ratio 0.25. Its lateral strain ϵ_{l} = 10^{- 3} . The elastic energy density of the wire is$ (1) $16 \times 10^{5} J m^{- 3}$ (2) $1 \times 10^{5} Im^{- 3}$ (3) $4 \times 10^{5} J m^{- 3}$ (4) $(8 \times 10^{5}) m^{- 3}$ 46. $A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by l . Another wire of same material of length 2L and radius 2r is pulled by a force 2f. Then the increase in its length will be:$ (1) $4 l$ (2) $\frac{l}{2}$ (3) $2 l$ (4) $l$ 47. $The approximate depth of an ocean is 2700 m. The compressibility of water is and density of water is . What fractional compression of water will be obtained at the bottom of the ocean?$ (1) $1.2 \times 10^{- 2}$ (2) $1.4 \times 10^{- 2}$ (3) $0.8 \times 10^{- 2}$ (4) $1.0 \times 10^{- 2}$ 48. $A metal rod of length L and cross-sectional area A is heated through T^{\circ} C . What is the force required to prevent the expansion of the rod lengthwise?$ (1) $\frac{YAαT}{( 1 - αT )}$ (2) $\frac{YAαT}{( 1 + αT )}$ (3) $\frac{( 1 - αT )}{YAαT}$ (4) $\frac{( 1 + αT )}{YAαT}$ 49. $A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to:$ (1) $r^{3}$ (2) $r^{4}$ (3) $r^{5}$ (4) $r^{2}$ 50. $A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:$ (1) $3.0 mm$ (2) $zero$ (3) $5.0 mm$ (4) $4.0$ 51. $The Young's modulus of a material is 2 \times 10^{11} N / m^{2} and its elastic limit is 1 \times 10^{8} N / m^{2} . For a wire of 1 m length of this material, the maximum elongation achievable is$ (1) $0.2 mm$ (2) $0.3 mm$ (3) $0.4 mm$ (4) $0.5 mm$ 52. $The electric field of light wave is given as E = 10^{3} cos (\frac{2 πx}{5 \times 10 ^{- 7}} - 2 π \times 6 \times 10^{14} t) x \frac{N}{C} This light falls on a metal plate of work function 2 eV . The stopping potential of the photo-electrons is: Given, E (in eV) = \frac{12375}{λ ( in Å )}$ (1) $2.0 V$ (2) $0.78 V$ (3) $0.48 V$ (4) $2.48 V$ 53. $A cylindrical rod made of aluminum has length 1 meter and diameter of 10 cm . The rod is subjected to a tensile force of 100 kN . The elongation in the rod is (Young's modulus of aluminum = 70 GPa)$ (1) $0.81 \times 10^{- 4} m$ (2) $2 \times 10^{- 4} m$ (3) $0.2\times 1 0^{- 4} m$ (4) $1.81 \times 10^{- 4} m$ 54. $'Young's modulus' is defined as the ratio of$ (1) $bulk stress and longitudinal strain$ (2) $hydraulic stress and hydraulic strain$ (3) $shearing stress and shearing strain$ (4) $tensile stress and longitudinal strain.$ 55. $A metal wire with circular cross section and length one meter is pulled with tensile force of 1000 N on each side. For the wire to be stretched not more than 0.25 cm, the minimum diameter of the wire required is (Young's modulus of the metal = 10^{11} Pa, take π = 1.77)$ (1) $1.13 mm$ (2) $2.26 mm$ (3) $4.12 mm$ (4) $3.1 mm$ 56. $A spring is stretched by applying a load to its free end. The strain produced in the spring is$ (1) $Volumetric$ (2) $Shear$ (3) $Longitudinal and Shear$ (4) $Longitudinal$ 57. $If a pressure of 8 \times 10^{8} Nm^{- 2} is applied to a lead block, so that its volume reduces by 20 % . The Bulk modulus of lead block is$ (1) $4 \times 10^{7} Nm^{- 2}$ (2) $4 \times 10^{8} Nm^{- 2}$ (3) $4 \times 10^{9} Nm^{- 2}$ (4) $4 \times 10^{10} Nm^{- 2}$ 58. $The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?$ (1) $L = 100 cm, r = 0.2 mm$ (2) $L = 200 cm, r = 0.4 mm$ (3) $L = 300 cm, r = 0.6 mm$ (4) $L = 400 cm, r = 0.8 mm$ 59. $An elastic spring under tension of 3 N has a length a . Its length is b under tension 2 N. For its length (3 a - 2 b), the value of tension will be______ N.$ 60. $The increase in pressure required to decrease the volume of a water sample by 0.2 % is P \times 10^{5} Nm^{- 2} . Bulk modulus of water is 2.15 \times 10^{9} Nm^{- 2} . The value of P is\dots..$