Mechanical Properties of Solids PYQs Set 4 (PDF)

Set 4 of 6 · Questions 91-120 of 156

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Mere Teacher · Previous Year Questions JEE Main Physics · Mechanical Properties of Solids · Set 4 (Q91-120)
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91. $A metallic bar of Young's modulus 0.5 \times 10^{11} Nm^{- 2} and coefficient of linear thermal expansion 10^{- 5}^{\circ} C^{- 1}, length 1 m and area of cross-section 10^{- 3} m^{2} is heated from 0^{\circ} C to 100^{\circ} C without expansion or bending. The compressive force developed in it is [NEET 2024]$ (1) $5 \times 10^{3} N$ (2) $50 \times 10^{3} N$ (3) $100 \times 10^{3} N$ (4) $2 \times 10^{3} N$ 92. $The length of a metal wire is l_{1} when the tension in it is F_{1} and l_{2} when the tension is F_{2} . Then, original length of the wire is$ (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) $\frac{l _{1} F _{1} - l _{2} F _{2}}{F _{2} - F _{1}}$ 93. $What should be the order of arrangement of de-Broglie wavelength of electron (λ_{e}), an α -particle (λ_{α}) and proton (λ_{p}) given that all have the same kinetic energy?$ (1) $λ_{e} = λ_{p} = λ_{α}$ (2) $λ_{e} < λ_{p} < λ_{α}$ (3) $λ_{e} > λ_{p} > λ_{α}$ (4) $λ_{e} = λ_{p} > λ_{α}$ 94. $The fractional change in the volume of a glass slab when subjected to hydraulic pressure of is (Bulk modulus of glass )$ (1) $1.44 \times 10^{- 5}$ (2) $3.54 \times 10^{- 5}$ (3) $2.74 \times 10^{- 5}$ (4) $3.14 \times 10^{- 5}$ 95. $Consider a rod of length 1.0 m with a cross-sectional area of 0.50 cm^{2} . The rod supports a 500 kg platform that hangs attached to the rod's lower end. What is elongation of the rod under the stress ignoring the weight of the rod? Consider the Young's modulus to be 10^{11} Pa and g = 10 m / s^{2} .$ (1) $2 mm$ (2) $0.5 mm$ (3) $1.5 mm$ (4) $1 mm$ 96. $Two metal wires ' P' and ' Q' of same length and material are stretched by same load. Their masses are in the ratio m_{1} : m_{2} . The ratio of elongations of wire ' P' to that of ' Q' is$ (1) $m_{1}^{2} : m_{2}^{2}$ (2) $m_{2}^{2} : m_{1}^{2}$ (3) $m_{2} : m_{1}$ (4) $m_{1} : m_{2}$ 97. $The maximum possible height of a mountain on earth is approximately (elastic limit of mountain rock = 30 \times 10^{7} Nm^{- 2}, average density of mountain rock = 3 \times 10^{3} kgm^{- 3}, g = 10 ms^{- 2})$ (1) $9 km$ (2) $10 km$ (3) $12 km$ (4) $8.8 km$ 98. $The ratio of the areas of cross sections of three wires in 1:2:3 and the ratio of the Young's modulii of their materials is 3 : 2 : 1 . If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is$ (1) $4:3:4$ (2) $1 : 1 : 1$ (3) $9 : 4 : 1$ (4) $3 : 4 : 3$ 99. $A rope 1 cm in diameter breaks if tension in it exceeds 500 N . The maximum tension that may be given to a similar rope of diameter 2 cm is$ (1) $2000 N$ (2) $1000 N$ (3) $500 N$ (4) $250 N$ 100. $One end of a steel rod of radius 10.0 mm and length 50.0 cm is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude 10.0 \times πkN . This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus = 2.0 \times \frac{10 ^{11} N}{m ^{2}})$ (1) $0.25 mm$ (2) $0.75 mm$ (3) $0.50 mm$ (4) $1.0 mm$ 101. $A copper wire of length 2.4 m and an aluminum wire of length 0.7 m, both having diameter 2 mm, are connected end to end. When stretched by a load, the obtained elongation is found to be 0.6 mm . The applied load is (Young's modulus of copper = 1.2 \times 10^{11} Nm^{- 2} and Young's modulus of aluminum = 0.7 \times 10^{11} Nm^{- 2})$ (1) $12 πN$ (2) $24 πN$ (3) $20 πN$ (4) $80 πN$ 102. $In a photoelectric experiment ultraviolet light of wavelength 280nm is used with lithium cathode having work function φ = 2.5 eV . If the wavelength of incident light is switched to 400nm, find out the change in the stopping potential. (h = 6.63 \times 1 0^{- 34} Js, c = 3 \times 1 0^{8} m s^{- 1})$ (1) $1.3V$ (2) $1.1V$ (3) $1.9V$ (4) $0.6V$ 103. $The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8 \times 10^{8} Nm^{- 2} and 2 \times 10^{11} Nm^{- 2}, is [NEET 2024]$ (1) $4 mm$ (2) $0.4 mm$ (3) $40 mm$ (4) $8 mm$ 104. $Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are Y_{1} and Y_{2}, respectively. The equivalent Young's modulus is$ (1) $Y_{1} + Y_{2}$ (2) $\frac{Y _{1} + Y _{2}}{2}$ (3) $\frac{Y _{1} Y _{2}}{Y _{1} + Y _{2}}$ (4) $Y_{1} Y_{2}$ 105. $The temperature of an ideal gas in 3-dimensions is 300K. The corresponding de-Broglie wavelength of the electron approximately at 300K, is: [m_{e} =mass of electron = 9 x 1 0^{- 31} kgh = Planck constant = 6. 6 x 1 0^{- 34} Js k_{B} =Boltzmann constant =1. 38 x 1 0^{- 23} J K^{- 1}]$ (1) $6.26nm$ (2) $8.46nm$ (3) $2.26nm$ (4) $3.25nm$ 106. $A pendulum suspended from a uniform wire of cross-sectional area A, has time period T. When an additional mass M is added to its bob, the time period changes to T_{M} . If the Young's modulus of the material of the wire is Y then \frac{1}{Y} is equal to: (g = gravitational acceleration)$ (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) $(1 - (\frac{T}{T _{M}})^{2}) \frac{A}{Mg}$ 107. $A slab of side 50 cm and thickness 10 cm is subjected to a shearing force of 10^{5} N on its narrow edge. If the lower edge is riveted to the floor and upper edge is displaced by 0.2 mm, then shear modulus of the material of the slab is$ (1) $6 GPa$ (2) $5 GPa$ (3) $4 GPa$ (4) $4. 5 GPa$ 108. $The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?$ (1) $D$ (2) $B$ (3) $C$ (4) $A$ 109. $Young's moduli of the material of wires A and B are in the ratio of 1 : 4, while its area of cross sections are in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]$ (1) $12 : 1$ (2) $1 : 36$ (3) $36 : 1$ (4) $1 : 12$ 110. $An aluminium rod with Young's modulus Y = 7. 0 x 1 0^{10} N m^{- 2} undergoes elastic strain of 0. 04%. The energy per unit volume stored in the rod in SI unit$ (1) $2800$ (2) $11200$ (3) $5600$ (4) $8400$ 111. $A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10^{5} N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement θ of the rod axis from its original position would be: (shear moduli, G = 10^{10} N / m^{2})$ (1) $1/160 π$ (2) $1/4 π$ (3) $1/40 π$ (4) $1/2 π$ 112. $Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is 1 \times 10^{11} N m^{- 2} . Original length of the wire is 2 m and the area of cross section is 2 cm^{2} . The wire will extend in length by_____μm .$ 113. $A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7 x 105 N m^{- 2} . The value of mass m is______kg. (Take g = 9. 8 m s^{- 2} and π = \frac{22}{7})$ 114. $The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of 7 \times 10^{6} Pa, would be mm^{3} . (Given bulk modulus of copper = 1.4 \times 10^{11} N m^{- 2})$ 115. $A particle of mass 9.1 \times 1 0^{- 31} kg travels in a medium with a speed of 1 0^{6} m / s and a photon of a radiation of linear momentum 1 0^{27} kgm / s travels in vacuum. The wavelength of photon is ___ times the wavelength of the particle.$ 116. $One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be_______[Area of cross section of wire = 0.005 cm^{2}, Y = 2 \times 10^{11} Nm^{- 2} and g = 10 ms^{- 2}]$ 117. $The density and breaking stress of a wire are 6 \times 10^{4} kg / m^{3} and 1.2 \times 10^{8} N / m^{2} respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \frac{1}{3} rd of the value on the surface of earth. The maximum length of the wire with breaking is ______m (take, (g = 10 m / s^{2}) .$ 118. $A uniform heavy rod of mass 20 kg. Cross sectional area 0.4 m^{2} and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x \times 1 0^{- 9} m . The value of x is_____.(Given. Young's modulus Y=2 x 1 0^{11} N m^{- 2} and g= 10 m s^{- 2})$ 119. $The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 x 1 0^{- 4} is .............kJ/ m^{3} . Assume that material is elastic upto the linear strain of 5 x 1 0^{4} .$ 120. $A light beam of wavelength 500nm is incident on a metal having work function of 1.25eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30cm. The value of B is x 1 0^{- 7} T Given hc = 20 \times 1 0^{- 26} J - m, mass of electron = 9 \times 1 0^{- 31} kg$