Mechanical Properties of Solids PYQs Set 2 (PDF)

Set 2 of 5 · Questions 31-60 of 125

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Mere Teacher · Previous Year Questions NEET Physics · Mechanical Properties of Solids · Set 2 (Q31-60)
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31. $A metallic rod breaks when strain produced is 0.2 % . The Young's modulus of the material of the rod is 7 \times 10^{9} N / m^{2} . The area of cross section to support a load of 10^{4} N is$ (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) $7.1 \times 10^{- 6} m^{2}$ 32. $Let a steel bar of length l, breadth b and depth d be loaded at the centre by a load W . Then the sag or bending of beam is (Y = Young's modulus of material of steel)$ (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) $\frac{W l ^{3}}{4 b d ^{2} Y}$ 33. $A steel rod of radius 20 mm and length of 2 m is acted upon by a force of 400 kN along the length. The values of stress and strain are respectively (Y_{steel} = 2 \times 10^{11} Nm^{- 2})$ (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) $4 \times 10^{8} Nm^{- 2}, 0.2 %$ 34. $The average depth of an oil well is . If the bulk modulus of oil is and the density of oil is . The fractional compression at the bottom of the well is (take, )$ (1) $3.75 %$ (2) $1.75 %$ (3) $2.75 %$ (4) $4.75 %$ 35. $Which of the following statement is incorrect?$ (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) $The reciprocal of the bulk modulus is called compressibility.$ 36. $The fractional compression of water at the depth of 2.5 km below the sea level is .Given, the Bulk modulus of water , density of water , acceleration due to gravity .$ (1) $1.25$ (2) $1.0$ (3) $1.75$ (4) $1.5$ 37. $The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?$ (1) $length = 100 cm, diameter = 1 mm$ (2) $length = 200 cm, diameter = 2 mm$ (3) $length = 300 cm, diameter = 3 mm$ (4) $length = 50 cm, diameter = 0.5 mm$ 38. $The increase in energy of a metal bar of length ' L' and cross-sectional area ' A' when compressed with a load ' M' along its length is (Y = Young's modulus of the material of metal bar)$ (1) $\frac{FL}{2 AY}$ (2) $\frac{F ^{2} L}{2 AY}$ (3) $\frac{FL}{AY}$ (4) $\frac{F ^{2} L ^{2}}{2 AY}$ 39. $The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is$ (1) $length 0.5 m, diameter 0.5 mm .$ (2) $length 1 m, diameter 1 mm .$ (3) $length 2 m, diameter 2 mm .$ (4) $length 3 m, diameter 3 mm .$ 40. $A copper wire and an aluminium wire have lengths in the ratio 5 : 2, diameters in the ratio 4 : 3 and forces applied in the ratio 4 : 5 . Find the ratio of increase in length of the copper wire to that aluminium wire. (Let Y_{Cu} = 1.1 \times 10^{11} Nm^{- 2}, Y_{Al} = 0.7 \times 10^{11} Nm^{- 2})$ (1) $\frac{176}{63}$ (2) $\frac{63}{88}$ (3) $\frac{189}{11}$ (4) $\frac{33}{89}$ 41. $A lift of mass m is connected to rope which is moving upward with maximum acceleration a . For maximum safe stress, the elastic limit of the rope is T . The minimum diameter of the rope is (g = gravitational acceleration)$ (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) $(\frac{m ( g + a )}{2 πT})^{1/2}$ 42. $Copper of fixed volume 'V' is drawn into wire of length 'λ'. When this wire is subjected to a constant force 'F', the extension produced in the wire is 'Δλ'. Which of the following graph is a straight line?$ (1) $Δλ versus 1/λ$ (2) $Δλ versus λ2$ (3) $Δλ versus 1/λ2$ (4) $Δλ versus λ$ 43. $A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 \times 1 0^{3} kg/ m^{3} and 2.2 \times 1 0^{11} N/ m^{2} respectively?$ (1) $188.5 Hz$ (2) $178.2 Hz$ (3) $200.5 Hz$ (4) $770 Hz$ 44. $A stretched wire of a material whose Young's modulus Y = 2 \times 10^{11} N m^{- 2} has Poisson's ratio 0.25. Its lateral strain ϵ_{l} = 10^{- 3} . The elastic energy density of the wire is$ (1) $16 \times 10^{5} J m^{- 3}$ (2) $1 \times 10^{5} Im^{- 3}$ (3) $4 \times 10^{5} J m^{- 3}$ (4) $(8 \times 10^{5}) m^{- 3}$ 45. $A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by l . Another wire of same material of length 2L and radius 2r is pulled by a force 2f. Then the increase in its length will be:$ (1) $4 l$ (2) $\frac{l}{2}$ (3) $2 l$ (4) $l$ 46. $The approximate depth of an ocean is 2700 m. The compressibility of water is and density of water is . What fractional compression of water will be obtained at the bottom of the ocean?$ (1) $1.2 \times 10^{- 2}$ (2) $1.4 \times 10^{- 2}$ (3) $0.8 \times 10^{- 2}$ (4) $1.0 \times 10^{- 2}$ 47. $A metal rod of length L and cross-sectional area A is heated through T^{\circ} C . What is the force required to prevent the expansion of the rod lengthwise?$ (1) $\frac{YAαT}{( 1 - αT )}$ (2) $\frac{YAαT}{( 1 + αT )}$ (3) $\frac{( 1 - αT )}{YAαT}$ (4) $\frac{( 1 + αT )}{YAαT}$ 48. $A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to:$ (1) $r^{3}$ (2) $r^{4}$ (3) $r^{5}$ (4) $r^{2}$ 49. $A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:$ (1) $3.0 mm$ (2) $zero$ (3) $5.0 mm$ (4) $4.0$ 50. $The Young's modulus of a material is 2 \times 10^{11} N / m^{2} and its elastic limit is 1 \times 10^{8} N / m^{2} . For a wire of 1 m length of this material, the maximum elongation achievable is$ (1) $0.2 mm$ (2) $0.3 mm$ (3) $0.4 mm$ (4) $0.5 mm$ 51. $The electric field of light wave is given as E = 10^{3} cos (\frac{2 πx}{5 \times 10 ^{- 7}} - 2 π \times 6 \times 10^{14} t) x \frac{N}{C} This light falls on a metal plate of work function 2 eV . The stopping potential of the photo-electrons is: Given, E (in eV) = \frac{12375}{λ ( in Å )}$ (1) $2.0 V$ (2) $0.78 V$ (3) $0.48 V$ (4) $2.48 V$ 52. $A cylindrical rod made of aluminum has length 1 meter and diameter of 10 cm . The rod is subjected to a tensile force of 100 kN . The elongation in the rod is (Young's modulus of aluminum = 70 GPa)$ (1) $0.81 \times 10^{- 4} m$ (2) $2 \times 10^{- 4} m$ (3) $0.2\times 1 0^{- 4} m$ (4) $1.81 \times 10^{- 4} m$ 53. $'Young's modulus' is defined as the ratio of$ (1) $bulk stress and longitudinal strain$ (2) $hydraulic stress and hydraulic strain$ (3) $shearing stress and shearing strain$ (4) $tensile stress and longitudinal strain.$ 54. $A metal wire with circular cross section and length one meter is pulled with tensile force of 1000 N on each side. For the wire to be stretched not more than 0.25 cm, the minimum diameter of the wire required is (Young's modulus of the metal = 10^{11} Pa, take π = 1.77)$ (1) $1.13 mm$ (2) $2.26 mm$ (3) $4.12 mm$ (4) $3.1 mm$ 55. $A spring is stretched by applying a load to its free end. The strain produced in the spring is$ (1) $Volumetric$ (2) $Shear$ (3) $Longitudinal and Shear$ (4) $Longitudinal$ 56. $If a pressure of 8 \times 10^{8} Nm^{- 2} is applied to a lead block, so that its volume reduces by 20 % . The Bulk modulus of lead block is$ (1) $4 \times 10^{7} Nm^{- 2}$ (2) $4 \times 10^{8} Nm^{- 2}$ (3) $4 \times 10^{9} Nm^{- 2}$ (4) $4 \times 10^{10} Nm^{- 2}$ 57. $The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?$ (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) $L = 400 cm, r = 0.8 mm$ 58. $A spherical ball of volume 2000 cm^{3} is subjected to a hydraulic pressure of 15 atm . If the change in volume is 5 \times 10^{- 2} cm^{3}, the bulk modules of the material of the spherical ball is (1 atm = 10^{5} Nm^{- 2})$ (1) $6 \times 10^{10} Nm^{- 2}$ (2) $2 \times 10^{10} Nm^{- 2}$ (3) $5 \times 10^{10} Nm^{- 2}$ (4) $15 \times 10^{10} Nm^{- 2}$ 59. $The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of$ (1) $4 : 1$ (2) $1 : 1$ (3) $1 : 2$ (4) $2 : 1$ 60. $The length of metallic wire is l_{1} when tension in it is T_{1} . It is l_{2} when the tension is T_{2} The original length of the wire will be:$ (1) $\frac{l _{1} + l _{2}}{2}$ (2) $\frac{T _{1} l _{1} - T _{2} l _{2}}{T _{2} - T _{1}}$ (3) $\frac{T _{2} l _{1} + T _{1} l _{2}}{T _{1} + T _{2}}$ (4) $\frac{T _{2} l _{1} - T _{1} l _{2}}{T _{2} - T _{1}}$