Mechanical Properties of Solids PYQs Set 4 (PDF)

Set 4 of 5 · Questions 91-120 of 125

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Mere Teacher · Previous Year Questions NEET Physics · Mechanical Properties of Solids · Set 4 (Q91-120)
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91. $The ratio of the areas of cross sections of three wires in 1:2:3 and the ratio of the Young's modulii of their materials is 3 : 2 : 1 . If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is$ (1) $4:3:4$ (2) $1 : 1 : 1$ (3) $9 : 4 : 1$ (4) $3 : 4 : 3$ 92. $A rope 1 cm in diameter breaks if tension in it exceeds 500 N . The maximum tension that may be given to a similar rope of diameter 2 cm is$ (1) $2000 N$ (2) $1000 N$ (3) $500 N$ (4) $250 N$ 93. $One end of a steel rod of radius 10.0 mm and length 50.0 cm is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude 10.0 \times πkN . This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus = 2.0 \times \frac{10 ^{11} N}{m ^{2}})$ (1) $0.25 mm$ (2) $0.75 mm$ (3) $0.50 mm$ (4) $1.0 mm$ 94. $A copper wire of length 2.4 m and an aluminum wire of length 0.7 m, both having diameter 2 mm, are connected end to end. When stretched by a load, the obtained elongation is found to be 0.6 mm . The applied load is (Young's modulus of copper = 1.2 \times 10^{11} Nm^{- 2} and Young's modulus of aluminum = 0.7 \times 10^{11} Nm^{- 2})$ (1) $12 πN$ (2) $24 πN$ (3) $20 πN$ (4) $80 πN$ 95. $In a photoelectric experiment ultraviolet light of wavelength 280nm is used with lithium cathode having work function φ = 2.5 eV . If the wavelength of incident light is switched to 400nm, find out the change in the stopping potential. (h = 6.63 \times 1 0^{- 34} Js, c = 3 \times 1 0^{8} m s^{- 1})$ (1) $1.3V$ (2) $1.1V$ (3) $1.9V$ (4) $0.6V$ 96. $The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8 \times 10^{8} Nm^{- 2} and 2 \times 10^{11} Nm^{- 2}, is [NEET 2024]$ (1) $4 mm$ (2) $0.4 mm$ (3) $40 mm$ (4) $8 mm$ 97. $Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are Y_{1} and Y_{2}, respectively. The equivalent Young's modulus is$ (1) $Y_{1} + Y_{2}$ (2) $\frac{Y _{1} + Y _{2}}{2}$ (3) $\frac{Y _{1} Y _{2}}{Y _{1} + Y _{2}}$ (4) $Y_{1} Y_{2}$ 98. $The temperature of an ideal gas in 3-dimensions is 300K. The corresponding de-Broglie wavelength of the electron approximately at 300K, is: [m_{e} =mass of electron = 9 x 1 0^{- 31} kgh = Planck constant = 6. 6 x 1 0^{- 34} Js k_{B} =Boltzmann constant =1. 38 x 1 0^{- 23} J K^{- 1}]$ (1) $6.26nm$ (2) $8.46nm$ (3) $2.26nm$ (4) $3.25nm$ 99. $A pendulum suspended from a uniform wire of cross-sectional area A, has time period T. When an additional mass M is added to its bob, the time period changes to T_{M} . If the Young's modulus of the material of the wire is Y then \frac{1}{Y} is equal to: (g = gravitational acceleration)$ (1) $((\frac{T _{M}}{T})^{2} - 1) \frac{A}{Mg}$ (2) $((\frac{T _{M}}{T})^{2} - 1) \frac{Mg}{A}$ (3) $(1 - (\frac{T _{M}}{T})^{2}) \frac{A}{Mg}$ (4) $(1 - (\frac{T}{T _{M}})^{2}) \frac{A}{Mg}$ 100. $A slab of side 50 cm and thickness 10 cm is subjected to a shearing force of 10^{5} N on its narrow edge. If the lower edge is riveted to the floor and upper edge is displaced by 0.2 mm, then shear modulus of the material of the slab is$ (1) $6 GPa$ (2) $5 GPa$ (3) $4 GPa$ (4) $4. 5 GPa$ 101. $The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?$ (1) $D$ (2) $B$ (3) $C$ (4) $A$ 102. $Young's moduli of the material of wires A and B are in the ratio of 1 : 4, while its area of cross sections are in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]$ (1) $12 : 1$ (2) $1 : 36$ (3) $36 : 1$ (4) $1 : 12$ 103. $An aluminium rod with Young's modulus Y = 7. 0 x 1 0^{10} N m^{- 2} undergoes elastic strain of 0. 04%. The energy per unit volume stored in the rod in SI unit$ (1) $2800$ (2) $11200$ (3) $5600$ (4) $8400$ 104. $A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10^{5} N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement θ of the rod axis from its original position would be: (shear moduli, G = 10^{10} N / m^{2})$ (1) $1/160 π$ (2) $1/4 π$ (3) $1/40 π$ (4) $1/2 π$ 105. $A monochromatic neon lamp with wavelength 670.5nm of illuminates a photo-sensitive material which has a stopping voltage of 0.48V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6nm?$ (1) $0.96V$ (2) $1.25V$ (3) $0.24V$ (4) $1.5V$ 106. $A moving proton and electron have the same DE Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option:$ (1) $Kp< Ke and Pp = Pe$ (2) $Kp = Ke and Pp = Pe$ (3) $Kp< Ke and Pp <Pe$ (4) $Kp>Ke and Pp = Pe$ 107. $The sag developed in a bar of length ' 1 ', breath ' b' and thickness 'd' when subjected to a load of ' w' at center is (Y - Young's modulus of the material of the bar)$ (1) $\frac{w ^{2} 1 ^{2}}{4 b d ^{2} Y}$ (2) $\frac{wl ^{3}}{bd ^{2} Y}$ (3) $\frac{w ^{3}}{4 b d ^{3} Y}$ (4) $None$ 108. $Two Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of$ (1) $2 : 1$ (2) $4 : 1$ (3) $1 : 1$ (4) $1 : 2$ 109. $One end of the steel rod is clamped to the roof and the other end is attached to a mass of 1000 kg as shown in the figure. The length of the rod is 50 cm and its crosssectional area is 1000 mm^{2} . The change in the length of the rod due to the weight of the mass is (Young's modulus of steel = 2 \times 10^{11} Nm^{- 2} and acceleration due to gravity = 10 ms^{- 2})$ (1) $0.025 mm$ (2) $0.10 mm$ (3) $0.050 mm$ (4) $. 0.075 mm$ 110. $Under isothermal condition, the pressure of a gas is given by P = a V^{- 3}, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to$ (1) $3P$ (2) $P$ (3) $2P$ (4) $\frac{P}{2}$ 111. $Two equal and opposite forces each F act on a rod of uniform cross-sectional area a as shown in the figure. Shearing stress on the section AB will be$ (1) $\frac{Fsin θcos θ}{a}$ (2) $\frac{Fsin θ}{a}$ (3) $\frac{Fcos θ}{a}$ (4) $\frac{F sin ^{2} θ}{a}$ 112. $The ratios of lengths, areas of cross-section and Young's modulii of steel to that of brass wires shown in the figure are a, b and c respectively. The ratio of increase in the lengths of brass to that of steel wires is [Assume that the masses of steel and brass wires are negligible]$ (1) $\frac{4 a}{7 bc}$ (2) $\frac{7 bc}{4 a}$ (3) $\frac{4 bc}{7 a}$ (4) $\frac{7 a}{4 bc}$ 113. $Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ∆ x on applying a force F, how much force is needed to stretch the second wire by the same amount$ (1) $9 F$ (2) $F$ (3) $4 F$ (4) $6 F$ 114. $The stopping potential V_{0} (in volt) as a function of frequency (v) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given: Planck's constant (h) = 6.63 \times 10^{- 34} Js electron charge (e = 1.6 \times 10^{- 19} C)$ (1) $1.82 eV$ (2) $1.66 eV$ (3) $1.95 eV$ (4) $2.12 eV$ 115. $Two small spherical metal balls, having equal masses, are made from materials of densities ρ_{1} and ρ_{2} (ρ_{1} = 8 ρ_{2}) and having radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0. 1 ρ_{2} . The ratio of their terminal velocities would be$ (1) $\frac{79}{72}$ (2) $\frac{19}{36}$ (3) $\frac{39}{72}$ (4) $\frac{79}{36}$ 116. $A force is applied to a steel wire 'A' rigidly clamped at one end. As a result elongation in the wire is 0.2 mm. If same force is applied to another steel wire 'B' of double the length and a diameter 2.4 times that of the wire 'A', the elongation in the wire B will be (wires having uniform circular cross sections)$ (1) $6.06x 1 0^{- 2} mm$ (2) $2.71 x 1 0^{- 2} mm$ (3) $3.0x 1 0^{- 2} mm$ (4) $6. 9 x 1 0^{- 2} mm$ 117. $Young's modulus experiment is performed on a steel wire of 1 m length and 8 mm diameter. The mass required to be added in the experiment to produce 5 mm elongation of the wire is (Y_{steel} = 2 \times 1 0^{9} Nm^{- 2}, g = 10 m / s^{2})$ (1) $25 kg$ (2) $50 kg$ (3) $250 kg$ (4) $500 kg$ 118. $A rectangular metallic block of dimensions 40 mm \times 20 mm when pulled with a tension of 50 k N undergoes only elastic deformation. The strain in the block is (The shear modulus of the material of the block is 40 \times 1 0^{9} N m^{- 2})$ (1) $1.56 \times 1 0^{- 3}$ (2) $2.4 \times 1 0^{- 3}$ (3) $3.2 \times 1 0^{- 3}$ (4) $1.08 \times 1 0^{- 3}$ 119. $An object of mass 15 kg is attached to the end of a metal wire of unstretched length 1.0 m . The object is then whirled in a vertical circle with an angular velocity of 4 rad / s at the bottom of the circle. If the cross sectional area of the wire is 0.05 cm^{2} and Young's modulus of metal is 2 \times 10^{11} N / m^{2}, then the elongation of the wire when the mass is at the lowest point of its path (Take g = 10 m / s^{2})$ (1) $0.27 mm$ (2) $0.39 mm$ (3) $0.55 mm$ (4) $0.25 mm$ 120. $An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 Å. What is the maximum kinetic energy of the emitted photoelectron?$ (1) $7.61eV$ (2) $1.41eV$ (3) $3.3eV$ (4) $No photoelectron would be emitted$