Mechanical Properties of Solids PYQs Set 5 (PDF)

Set 5 of 6 · Questions 121-150 of 156

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Mere Teacher · Previous Year Questions JEE Main Physics · Mechanical Properties of Solids · Set 5 (Q121-150)
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121. $A monochromatic neon lamp with wavelength 670.5nm of illuminates a photo-sensitive material which has a stopping voltage of 0.48V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6nm?$ (1) $0.96V$ (2) $1.25V$ (3) $0.24V$ (4) $1.5V$ 122. $A moving proton and electron have the same DE Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option:$ (1) $Kp< Ke and Pp = Pe$ (2) $Kp = Ke and Pp = Pe$ (3) $Kp< Ke and Pp <Pe$ (4) $Kp>Ke and Pp = Pe$ 123. $The sag developed in a bar of length ' 1 ', breath ' b' and thickness 'd' when subjected to a load of ' w' at center is (Y - Young's modulus of the material of the bar)$ (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) $None$ 124. $Two Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of$ (1) $2 : 1$ (2) $4 : 1$ (3) $1 : 1$ (4) $1 : 2$ 125. $One end of the steel rod is clamped to the roof and the other end is attached to a mass of 1000 kg as shown in the figure. The length of the rod is 50 cm and its crosssectional area is 1000 mm^{2} . The change in the length of the rod due to the weight of the mass is (Young's modulus of steel = 2 \times 10^{11} Nm^{- 2} and acceleration due to gravity = 10 ms^{- 2})$ (1) $0.025 mm$ (2) $0.10 mm$ (3) $0.050 mm$ (4) $. 0.075 mm$ 126. $Under isothermal condition, the pressure of a gas is given by P = a V^{- 3}, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to$ (1) $3P$ (2) $P$ (3) $2P$ (4) $\frac{P}{2}$ 127. $Two equal and opposite forces each F act on a rod of uniform cross-sectional area a as shown in the figure. Shearing stress on the section AB will be$ (1) $\frac{Fsin θcos θ}{a}$ (2) $\frac{Fsin θ}{a}$ (3) $\frac{Fcos θ}{a}$ (4) $\frac{F sin ^{2} θ}{a}$ 128. $The ratios of lengths, areas of cross-section and Young's modulii of steel to that of brass wires shown in the figure are a, b and c respectively. The ratio of increase in the lengths of brass to that of steel wires is [Assume that the masses of steel and brass wires are negligible]$ (1) $\frac{4 a}{7 bc}$ (2) $\frac{7 bc}{4 a}$ (3) $\frac{4 bc}{7 a}$ (4) $\frac{7 a}{4 bc}$ 129. $Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ∆ x on applying a force F, how much force is needed to stretch the second wire by the same amount$ (1) $9 F$ (2) $F$ (3) $4 F$ (4) $6 F$ 130. $The stopping potential V_{0} (in volt) as a function of frequency (v) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given: Planck's constant (h) = 6.63 \times 10^{- 34} Js electron charge (e = 1.6 \times 10^{- 19} C)$ (1) $1.82 eV$ (2) $1.66 eV$ (3) $1.95 eV$ (4) $2.12 eV$ 131. $Two small spherical metal balls, having equal masses, are made from materials of densities ρ_{1} and ρ_{2} (ρ_{1} = 8 ρ_{2}) and having radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0. 1 ρ_{2} . The ratio of their terminal velocities would be$ (1) $\frac{79}{72}$ (2) $\frac{19}{36}$ (3) $\frac{39}{72}$ (4) $\frac{79}{36}$ 132. $A force is applied to a steel wire 'A' rigidly clamped at one end. As a result elongation in the wire is 0.2 mm. If same force is applied to another steel wire 'B' of double the length and a diameter 2.4 times that of the wire 'A', the elongation in the wire B will be (wires having uniform circular cross sections)$ (1) $6.06x 1 0^{- 2} mm$ (2) $2.71 x 1 0^{- 2} mm$ (3) $3.0x 1 0^{- 2} mm$ (4) $6. 9 x 1 0^{- 2} mm$ 133. $Young's modulus experiment is performed on a steel wire of 1 m length and 8 mm diameter. The mass required to be added in the experiment to produce 5 mm elongation of the wire is (Y_{steel} = 2 \times 1 0^{9} Nm^{- 2}, g = 10 m / s^{2})$ (1) $25 kg$ (2) $50 kg$ (3) $250 kg$ (4) $500 kg$ 134. $A rectangular metallic block of dimensions 40 mm \times 20 mm when pulled with a tension of 50 k N undergoes only elastic deformation. The strain in the block is (The shear modulus of the material of the block is 40 \times 1 0^{9} N m^{- 2})$ (1) $1.56 \times 1 0^{- 3}$ (2) $2.4 \times 1 0^{- 3}$ (3) $3.2 \times 1 0^{- 3}$ (4) $1.08 \times 1 0^{- 3}$ 135. $An object of mass 15 kg is attached to the end of a metal wire of unstretched length 1.0 m . The object is then whirled in a vertical circle with an angular velocity of 4 rad / s at the bottom of the circle. If the cross sectional area of the wire is 0.05 cm^{2} and Young's modulus of metal is 2 \times 10^{11} N / m^{2}, then the elongation of the wire when the mass is at the lowest point of its path (Take g = 10 m / s^{2})$ (1) $0.27 mm$ (2) $0.39 mm$ (3) $0.55 mm$ (4) $0.25 mm$ 136. $An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 Å. What is the maximum kinetic energy of the emitted photoelectron?$ (1) $7.61eV$ (2) $1.41eV$ (3) $3.3eV$ (4) $No photoelectron would be emitted$ 137. $Let a wire be suspended from the ceiling (rigid support) and stretched by a weight w attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is [NEET 2023]$ (1) $w / A$ (2) $w /2 A$ (3) $zero$ (4) $2 w / A$ 138. $As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be x x 1 0^{4} N m^{- 2} . The value of x is_____.$ 139. $A thin rod having a length of 1 m and area of cross-section 3 x 1 0^{- 6} m^{2} is suspended vertically from one end. The rod is cooled from 210°C to 160°C After cooling, a mass M is attached at the lower end of the rod such that the length of rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the rod are 2 x 1 0^{11} N m^{- 2} and 2 x 1 0^{- 5} K^{- 1}, respectively. The value of M is______kg. (Take g = 10 m s^{- 2})$ 140. $Two wires each of radius 0. 2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is______1 0^{- 6} m. [Young's modulus for steel = 2 x 1 0^{11} N m^{- 2} and g = 10 m s^{- 2}]$ 141. $A wire of cross-sectional area A, modulus of elasticity 2 \times 10^{11} Nm^{- 2} and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle θ = \frac{1}{100} radian on the points of support. The value of A is ______\times 10^{- 4} m^{2} (consider x << L). (given: g = 10 m / s^{2})$ 142. $A certain metallic surface is illuminated by monochromatic radiation of wavelength λ . The stopping potential for photoelectric current for this radiation is 3 V_{0} . If the same surface is illuminated with a radiation of wavelength 2 λ, the stopping potential is V_{0} . The threshold wavelength of this surface for photoelectric effect is ____λ$ 143. $A steel rod has a radius of 20 mm and a length of 2. 0 m. A force of 62. 8 kN stretches it along its length. Young's modulus of steel is 2. 0 x 1 0^{11} N m^{- 2} . The longitudinal strain produced in the wire is__________x 1 0^{- 5} .$ 144. $The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is_____m m^{2} . (Given, Y = 2.0 x 1 0^{11} N m^{- 2})$ 145. $Each of three blocks P, Q and R shown in figure has a mass of 3 kg . Each of the wire A and B has crosssectional area 0.005 cm^{2} and Young's modulus 2 \times 10^{11} N m^{- 2} . Neglecting friction, the longitudinal strain on wire B is______\times 10^{- 4} . (Take (g = 10 \frac{m}{s ^{2}})$ 146. $In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x x 1 0^{11} N m^{- 2}, then the value of x is________.$ 147. $In an experiment of determine the Young's modulus of wire of a length exactly 1m, the extension in the length of the wire is measured as 0.4mm with an uncertainty of \pm0.02 mm when a load of 1kg is applied. The diameter of the wire is measured as 0.4mm with an uncertainty of \pm0.01 mm. The error in the measurement of Young's modulus (^{∆ Y}) is found to be x \times 1 0^{10} N m^{- 2} . The value of x is _______ [Take g = 10m/ s^{2}]$ 148. $A metal wire of length 0.5 m and cross-sectional area 1 0^{- 4} m^{2} has breaking stress 5 \times 1 0^{8} N m^{- 2} . A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be ____m s^{- 1} .$ 149. $Two slabs with square cross section of different materials (1, 2) with equal sides (l) and thickness d_{1} and d_{2} such that d_{2} = 2 d_{1} and l > d_{2} . Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is θ_{2} = 2 θ_{1} . If the shear moduli of material 1 is 4 \times 10^{9} N / m^{2}, then shear moduli of material 2 is x \times 10^{9} N / m^{2}, where value of x is__________.$ 150. $A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ______cm.$