Mechanical Properties of Solids PYQs Set 3 (PDF)

Set 3 of 6 · Questions 61-90 of 156

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Mere Teacher · Previous Year Questions JEE Main Physics · Mechanical Properties of Solids · Set 3 (Q61-90)
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61. $A spherical ball of volume 2000 cm^{3} is subjected to a hydraulic pressure of 15 atm . If the change in volume is 5 \times 10^{- 2} cm^{3}, the bulk modules of the material of the spherical ball is (1 atm = 10^{5} Nm^{- 2})$ (1) $6 \times 10^{10} Nm^{- 2}$ (2) $2 \times 10^{10} Nm^{- 2}$ (3) $5 \times 10^{10} Nm^{- 2}$ (4) $15 \times 10^{10} Nm^{- 2}$ 62. $The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of$ (1) $4 : 1$ (2) $1 : 1$ (3) $1 : 2$ (4) $2 : 1$ 63. $The length of metallic wire is l_{1} when tension in it is T_{1} . It is l_{2} when the tension is T_{2} The original length of the wire will be:$ (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) $\frac{T _{2} l _{1} - T _{1} l _{2}}{T _{2} - T _{1}}$ 64. $The bulk modulus of a liquid is 3 x 1 0^{10} N m^{- 2} . The pressure required to reduce the volume of liquid by 2% is:$ (1) $3 x 1 0^{8} N m^{- 2}$ (2) $9 x 1 0^{8} N m^{- 2}$ (3) $6 x 1 0^{8} N m^{- 2}$ (4) $12 x 1 0^{8} N m^{- 2}$ 65. $If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any materialrespectively. Choose the correct relation for these parameters.$ (1) $K = \frac{Y η}{9 η - 3 Y} N / m^{2}$ (2) $η = \frac{3 Y K}{9 K + Y} N / m^{2}$ (3) $Y = \frac{9 K η}{3 K - η} N / m^{2}$ (4) $Y = \frac{9 K η}{2 η + 3 K} N / m^{2}$ 66. $The volume of a material reduces by 2 % when the pressure is increased from 1 atm to 2 atm . What is it's bulk modulus?$ (1) $10^{5} N / m^{2}$ (2) $5 \times 10^{5} N / m^{2}$ (3) $10^{6} N / m^{2}$ (4) $5 \times 10^{6} N / m^{2}$ 67. $When radiation of wavelength λ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6V. The threshold wavelength of the metal is:$ (1) $2 λ$ (2) $4 λ$ (3) $8 λ$ (4) $6 λ$ 68. $One end of a wire of 8 mm radius and 100 cm length is fixed and the other end is twisted through an angle of 45^{\circ} . The angle of shear is$ (1) $0.36^{\circ}$ (2) $0.12^{\circ}$ (3) $3.6^{\circ}$ (4) $1.2^{\circ}$ 69. $A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 \times 10^{7} Nm^{- 2} . The area of crosssection from the wire is 10^{- 6} m^{2} . The maximum angular velocity with which it can be rotated in a horizontal circle is$ (1) $4 rad s^{- 1}$ (2) $8 rad s^{- 1}$ (3) $16 rad s^{- 1}$ (4) $32 rad s^{- 1}$ 70. $A rod, of length L at room temperature and uniform area of cross section A, is made a metal having coefficient of linear expansion α/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by ∆ T K. Young's modulus, Y, for this metal is:$ (1) $\frac{2 F}{Aα Δ T}$ (2) $\frac{F}{Aα ( Δ T - 273 )}$ (3) $\frac{F}{Aα Δ T}$ (4) $\frac{F}{2 Aα Δ T}$ 71. $Two identical wires of substance ' P' and ' Q' are subjected to equal stretching force along the length. If the elongation of ' Q' is more than that of ' P', then$ (1) $both P and Q are equally elastic$ (2) $P is more elastic than Q$ (3) $P is plastic and Q is elastic$ (4) $Q is more elastic than P .$ 72. $Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1 : 3 . The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is$ (1) $3 : 1$ (2) $9 : 1$ (3) $27 : 1$ (4) $81 : 1$ 73. $A wire of length L and area of cross section A is made of material of Young's modulus Y . It is stretched by an amount x . The work done in stretching the wire is$ (1) $\frac{Y x ^{2} A}{2 L}$ (2) $\frac{2 Y x ^{2} A}{L}$ (3) $\frac{YxA}{2 L}$ (4) $\frac{Y x ^{2} A}{2}$ 74. $Two wires are made of the same material and have the same volume. The first wire has cross-sectional area and the second wire has cross-sectional area 3 A . If the length of the first wire is increased by Δ l on applying a force F, how much force is needed to stretch the second wire by the same amount? [NEET 2018]$ (1) $4 F$ (2) $6 F$ (3) $9 F$ (4) $F$ 75. $Which of the following substances has the highest elasticity?$ (1) $Sponge$ (2) $Steel$ (3) $Rubber$ (4) $Copper$ 76. $A steel rod has a radius of 10 mm and a length of 1 m . A 80 kN force stretches it along its length. If the Young's modulus of the rod is 2 \times 10^{11} N / m^{2}, then the change in length is$ (1) $\frac{2}{π} mm$ (2) $\frac{4}{π} mm$ (3) $\frac{3}{π} mm$ (4) $1 mm$ 77. $Two wires A and B are stretched by the same load. If the area of cross-section of wire A is double that of B, then the stress on B is$ (1) $equal to that on A$ (2) $twice that on A$ (3) $half that on A$ (4) $four times that on A .$ 78. $The elastic limit of a metal is \frac{400}{π} MPa . If a rod of this metal is to support a 484 N load without exceeding its elastic limit, the minimum diameter of the rod is$ (1) $2.2 mm$ (2) $1.2 mm$ (3) $2 mm$ (4) $1.6 mm$ 79. $The lengths of four wires A, B, C and D made of same material are 1 m, 2 m, 3 m and 4 m respectively. The radii of the wires A, B, C and D are 0.2 mm, 0.4 mm, 0.6 mm and 0.8 mm respectively. For the same applied tension, the elongation is more in the wire.$ (1) $A$ (2) $B$ (3) $C$ (4) $D$ 80. $When a load of 80 N is suspended from a string, its length is 101 mm . If a load of 100 N is suspended, its length is 102 mm . If a load of 160 N is suspended from it, then length of the string is (Assume the area of cross-section unchanged)$ (1) $15.5 cm$ (2) $13.5 cm$ (3) $16.5 cm$ (4) $10.5 cm$ 81. $Work done in stretching a wire through 1 mm is 2 J . What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross section by 1 mm ?$ (1) $2 J$ (2) $4 J$ (3) $8 J$ (4) $16 J$ 82. $The Young's modulus of a rubber string of length 12 cm and density 1.5 kgm^{- 3} is 5 \times 10^{8} Nm^{- 2} . When this string is suspended vertically, the increase in its length due to its own weight is. (Take, g = 10 ms^{- 2})$ (1) $2.16 \times 10^{- 10} m$ (2) $9.6 \times 10^{- 11} m$ (3) $9.6 \times 10^{- 3} m$ (4) $2.16 \times 10^{- 3} m$ 83. $For a solid rod, the Young's modulus of elasticity is 3.2 x 1 0^{11} N m^{- 2} and density is 8 x 1 0^{3} kg m^{- 3} . The velocity of longitudinal wave in the rod will be.$ (1) $145.75 x 1 0^{3} m s^{- 1}$ (2) $3.65 x 10 m s^{- 1}$ (3) $18. 96 x 1 0^{3} m s^{- 1}$ (4) $6.32 x 1 0^{3} m s^{- 1}$ 84. $The bulk modulus of a spherical object is . If it is subjected to uniform pressure , the fractional decrease in radius is [NEET 2017]$ (1) $\frac{p}{B}$ (2) $\frac{B}{3 p}$ (3) $\frac{3 p}{B}$ (4) $\frac{p}{3 B}$ 85. $Each side of a box made of metal sheet in cubic shape is ’ a ’ at room temperature ’ T ’, the coefficient of linearexpansion of the metal sheet is ’ α^{’} . The metal sheet is heated uniformly, by a small temperature Δ T, so thatits new temperature is T + Δ T . Calculate the increase in thevolume of the metal box-$ (1) $\frac{4}{3} π a^{3} α Δ T$ (2) $4 π a^{3} α Δ T$ (3) $3 a^{3} α Δ T$ (4) $4 a^{3} α Δ T$ 86. $The pressure required to decrease the volume of 4000 cc water by 0.05 % is (Bulk modulus of water = 2.2 \times 10^{9} Nm^{- 2})$ (1) $11 \times 10^{6} Nm^{- 2}$ (2) $5 \times 10^{5} Nm^{- 2}$ (3) $2.2 \times 10^{6} Nm^{- 2}$ (4) $1.1 \times 10^{6} Nm^{- 2}$ 87. $If average depth of an ocean is and the bulk modulus of water is , then fractional compression of water at the bottom of ocean is . The value of is_____ (Given, )$ 88. $The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02 % is______m . (Take density of sea water = 10^{3} kgm^{- 3}, Bulk modulus of rubber = 9 \times 10^{8} Nm^{- 2}, and g = 10 ms^{- 2})$ 89. $Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4 : 1 and force F_{1} is applied to P, an extension of Δ l is produced. The force which is required to produce same extension in Q is F_{2} . The value of \frac{F _{1}}{F _{2}} is________$ 90. $A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm^{3} . If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was liter. (Take (1 atm = 10^{5} Pa)$