Mechanical Properties of Solids PYQs Set 3 (PDF)

Set 3 of 5 · Questions 61-90 of 125

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Mere Teacher · Previous Year Questions NEET Physics · Mechanical Properties of Solids · Set 3 (Q61-90)
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61. $The bulk modulus of a liquid is 3 x 1 0^{10} N m^{- 2} . The pressure required to reduce the volume of liquid by 2% is:$ (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) $12 x 1 0^{8} N m^{- 2}$ 62. $If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any materialrespectively. Choose the correct relation for these parameters.$ (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) $Y = \frac{9 K η}{2 η + 3 K} N / m^{2}$ 63. $The volume of a material reduces by 2 % when the pressure is increased from 1 atm to 2 atm . What is it's bulk modulus?$ (1) $10^{5} N / m^{2}$ (2) $5 \times 10^{5} N / m^{2}$ (3) $10^{6} N / m^{2}$ (4) $5 \times 10^{6} N / m^{2}$ 64. $When radiation of wavelength λ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6V. The threshold wavelength of the metal is:$ (1) $2 λ$ (2) $4 λ$ (3) $8 λ$ (4) $6 λ$ 65. $One end of a wire of 8 mm radius and 100 cm length is fixed and the other end is twisted through an angle of 45^{\circ} . The angle of shear is$ (1) $0.36^{\circ}$ (2) $0.12^{\circ}$ (3) $3.6^{\circ}$ (4) $1.2^{\circ}$ 66. $A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 \times 10^{7} Nm^{- 2} . The area of crosssection from the wire is 10^{- 6} m^{2} . The maximum angular velocity with which it can be rotated in a horizontal circle is$ (1) $4 rad s^{- 1}$ (2) $8 rad s^{- 1}$ (3) $16 rad s^{- 1}$ (4) $32 rad s^{- 1}$ 67. $A rod, of length L at room temperature and uniform area of cross section A, is made a metal having coefficient of linear expansion α/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by ∆ T K. Young's modulus, Y, for this metal is:$ (1) $\frac{2 F}{Aα Δ T}$ (2) $\frac{F}{Aα ( Δ T - 273 )}$ (3) $\frac{F}{Aα Δ T}$ (4) $\frac{F}{2 Aα Δ T}$ 68. $Two identical wires of substance ' P' and ' Q' are subjected to equal stretching force along the length. If the elongation of ' Q' is more than that of ' P', then$ (1) $both P and Q are equally elastic$ (2) $P is more elastic than Q$ (3) $P is plastic and Q is elastic$ (4) $Q is more elastic than P .$ 69. $Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1 : 3 . The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is$ (1) $3 : 1$ (2) $9 : 1$ (3) $27 : 1$ (4) $81 : 1$ 70. $A wire of length L and area of cross section A is made of material of Young's modulus Y . It is stretched by an amount x . The work done in stretching the wire is$ (1) $\frac{Y x ^{2} A}{2 L}$ (2) $\frac{2 Y x ^{2} A}{L}$ (3) $\frac{YxA}{2 L}$ (4) $\frac{Y x ^{2} A}{2}$ 71. $Two wires are made of the same material and have the same volume. The first wire has cross-sectional area and the second wire has cross-sectional area 3 A . If the length of the first wire is increased by Δ l on applying a force F, how much force is needed to stretch the second wire by the same amount? [NEET 2018]$ (1) $4 F$ (2) $6 F$ (3) $9 F$ (4) $F$ 72. $Which of the following substances has the highest elasticity?$ (1) $Sponge$ (2) $Steel$ (3) $Rubber$ (4) $Copper$ 73. $A steel rod has a radius of 10 mm and a length of 1 m . A 80 kN force stretches it along its length. If the Young's modulus of the rod is 2 \times 10^{11} N / m^{2}, then the change in length is$ (1) $\frac{2}{π} mm$ (2) $\frac{4}{π} mm$ (3) $\frac{3}{π} mm$ (4) $1 mm$ 74. $Two wires A and B are stretched by the same load. If the area of cross-section of wire A is double that of B, then the stress on B is$ (1) $equal to that on A$ (2) $twice that on A$ (3) $half that on A$ (4) $four times that on A .$ 75. $The elastic limit of a metal is \frac{400}{π} MPa . If a rod of this metal is to support a 484 N load without exceeding its elastic limit, the minimum diameter of the rod is$ (1) $2.2 mm$ (2) $1.2 mm$ (3) $2 mm$ (4) $1.6 mm$ 76. $The lengths of four wires A, B, C and D made of same material are 1 m, 2 m, 3 m and 4 m respectively. The radii of the wires A, B, C and D are 0.2 mm, 0.4 mm, 0.6 mm and 0.8 mm respectively. For the same applied tension, the elongation is more in the wire.$ (1) $A$ (2) $B$ (3) $C$ (4) $D$ 77. $When a load of 80 N is suspended from a string, its length is 101 mm . If a load of 100 N is suspended, its length is 102 mm . If a load of 160 N is suspended from it, then length of the string is (Assume the area of cross-section unchanged)$ (1) $15.5 cm$ (2) $13.5 cm$ (3) $16.5 cm$ (4) $10.5 cm$ 78. $Work done in stretching a wire through 1 mm is 2 J . What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross section by 1 mm ?$ (1) $2 J$ (2) $4 J$ (3) $8 J$ (4) $16 J$ 79. $The Young's modulus of a rubber string of length 12 cm and density 1.5 kgm^{- 3} is 5 \times 10^{8} Nm^{- 2} . When this string is suspended vertically, the increase in its length due to its own weight is. (Take, g = 10 ms^{- 2})$ (1) $2.16 \times 10^{- 10} m$ (2) $9.6 \times 10^{- 11} m$ (3) $9.6 \times 10^{- 3} m$ (4) $2.16 \times 10^{- 3} m$ 80. $For a solid rod, the Young's modulus of elasticity is 3.2 x 1 0^{11} N m^{- 2} and density is 8 x 1 0^{3} kg m^{- 3} . The velocity of longitudinal wave in the rod will be.$ (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) $6.32 x 1 0^{3} m s^{- 1}$ 81. $The bulk modulus of a spherical object is . If it is subjected to uniform pressure , the fractional decrease in radius is [NEET 2017]$ (1) $\frac{p}{B}$ (2) $\frac{B}{3 p}$ (3) $\frac{3 p}{B}$ (4) $\frac{p}{3 B}$ 82. $Each side of a box made of metal sheet in cubic shape is ’ a ’ at room temperature ’ T ’, the coefficient of linearexpansion of the metal sheet is ’ α^{’} . The metal sheet is heated uniformly, by a small temperature Δ T, so thatits new temperature is T + Δ T . Calculate the increase in thevolume of the metal box-$ (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) $4 a^{3} α Δ T$ 83. $The pressure required to decrease the volume of 4000 cc water by 0.05 % is (Bulk modulus of water = 2.2 \times 10^{9} Nm^{- 2})$ (1) $11 \times 10^{6} Nm^{- 2}$ (2) $5 \times 10^{5} Nm^{- 2}$ (3) $2.2 \times 10^{6} Nm^{- 2}$ (4) $1.1 \times 10^{6} Nm^{- 2}$ 84. $A metallic bar of Young's modulus 0.5 \times 10^{11} Nm^{- 2} and coefficient of linear thermal expansion 10^{- 5}^{\circ} C^{- 1}, length 1 m and area of cross-section 10^{- 3} m^{2} is heated from 0^{\circ} C to 100^{\circ} C without expansion or bending. The compressive force developed in it is [NEET 2024]$ (1) $5 \times 10^{3} N$ (2) $50 \times 10^{3} N$ (3) $100 \times 10^{3} N$ (4) $2 \times 10^{3} N$ 85. $The length of a metal wire is l_{1} when the tension in it is F_{1} and l_{2} when the tension is F_{2} . Then, original length of the wire is$ (1) $\frac{l _{1} F _{1} + l _{2} F _{2}}{F _{1} + F _{2}}$ (2) $\frac{l _{2} - l _{1}}{F _{2} - F _{1}}$ (3) $\frac{l _{1} F _{2} - l _{2} F _{1}}{F _{2} - F _{1}}$ (4) $\frac{l _{1} F _{1} - l _{2} F _{2}}{F _{2} - F _{1}}$ 86. $What should be the order of arrangement of de-Broglie wavelength of electron (λ_{e}), an α -particle (λ_{α}) and proton (λ_{p}) given that all have the same kinetic energy?$ (1) $λ_{e} = λ_{p} = λ_{α}$ (2) $λ_{e} < λ_{p} < λ_{α}$ (3) $λ_{e} > λ_{p} > λ_{α}$ (4) $λ_{e} = λ_{p} > λ_{α}$ 87. $The fractional change in the volume of a glass slab when subjected to hydraulic pressure of is (Bulk modulus of glass )$ (1) $1.44 \times 10^{- 5}$ (2) $3.54 \times 10^{- 5}$ (3) $2.74 \times 10^{- 5}$ (4) $3.14 \times 10^{- 5}$ 88. $Consider a rod of length 1.0 m with a cross-sectional area of 0.50 cm^{2} . The rod supports a 500 kg platform that hangs attached to the rod's lower end. What is elongation of the rod under the stress ignoring the weight of the rod? Consider the Young's modulus to be 10^{11} Pa and g = 10 m / s^{2} .$ (1) $2 mm$ (2) $0.5 mm$ (3) $1.5 mm$ (4) $1 mm$ 89. $Two metal wires ' P' and ' Q' of same length and material are stretched by same load. Their masses are in the ratio m_{1} : m_{2} . The ratio of elongations of wire ' P' to that of ' Q' is$ (1) $m_{1}^{2} : m_{2}^{2}$ (2) $m_{2}^{2} : m_{1}^{2}$ (3) $m_{2} : m_{1}$ (4) $m_{1} : m_{2}$ 90. $The maximum possible height of a mountain on earth is approximately (elastic limit of mountain rock = 30 \times 10^{7} Nm^{- 2}, average density of mountain rock = 3 \times 10^{3} kgm^{- 3}, g = 10 ms^{- 2})$ (1) $9 km$ (2) $10 km$ (3) $12 km$ (4) $8.8 km$