Units, Dimensions & Measurements PYQs Set 4 (PDF)

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Set 4 of 10 · Questions 91-120 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 4 (Q91-120)
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91. $If the dimensions of a physical quantity are given by MLT, then the physical quantity will be$ (1) $velocity if a = 1, b = 0, c = - 1$ (2) $acceleration if a = 1, b = 1, c = - 2$ (3) $force if a = 0, b = - 1, c = - 2$ (4) $pressure if a = 1, b = - 1, c = - 2$ 92. $Consider an expression QV = kpT L^{α}, where V, p, T, L are volume, pressure, time and length respectively. The quantity [Q] has dimension M L^{- 1} T^{- 1} and k is dimensionless constant. The value of integer α is$ (1) $2$ (2) $-2$ (3) $3$ (4) $-1$ 93. $The pressure on a circular plate is measured by measuring the force on the plate and the radius of the plate. If the errors in measurement of the force and the radius are 5 % and 3 % respectively, the percentage of error in the measurement of pressure is$ (1) $8$ (2) $14$ (3) $11$ (4) $12$ 94. $Which of the following is a dimensional constant?$ (1) $Relative density$ (2) $Gravitational constant$ (3) $Refractive index$ (4) $Poisson ratio$ 95. $Which of the following equations is dimensionally incorrect? Where t=time, h=height, s=surface tension, θ = angle, ρ =density, a, r = radius, g=acceleration due to gravity, v=volume, p=pressure, W=work done, Γ = torque, permittivity, electric field, J=current density, L=length.$ (1) $v = \frac{π p a ^{4}}{8 η L}$ (2) $h = \frac{2 scos θ}{ρ r g}$ (3) $J =\in \frac{\partial E}{\partial t}$ (4) $W = Γ θ$ 96. $The resistance R = \frac{V}{I} where V = (100 \pm 5) V and I = (10 \pm 0.2) A . The percentage error in R is$ (1) $5.2 %$ (2) $4.8 %$ (3) $7 %$ (4) $3 %$ 97. $The force F acting on a body of density d are related by the relation F = \frac{y}{d} . The dimensions of y are$ (1) $L^{- 1/2} M^{3/2} T^{- 2}$ (2) $L^{- 1} M^{1/2} T^{- 2}$ (3) $L^{- 1} M^{3/2} T^{- 2}$ (4) $L^{- 1/2} M^{1/2} T^{- 2}$ 98. $Least count of a vernier caliper is \frac{1}{20 N} cm . The value of one division on the main scale is 1 mm . Then the number of divisions of main scale that coincide with N divisions of vernier scale is:$ (1) $(2 N - 1)$ (2) $(\frac{2 N - 1}{2 N})$ (3) $(\frac{2 N - 1}{2})$ (4) $(\frac{2 N - 1}{20 N})$ 99. $If Surface tension (S), Moment of Inertia (I) and Planck'sconstant (h), were to be taken as the fundamental units,then dimensional formula for linear momentum would be :$ (1) $S^{1/2} I^{3/2} h^{- 1}$ (2) $S^{1/2} I^{1/2} h^{- 1}$ (3) $S^{1/2} I^{1/2} h^{0}$ (4) $S^{3/2} I^{1/2} h^{0}$ 100. $The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are [NEET 2023]$ (1) $personal errors$ (2) $least count errors$ (3) $random error$ (4) $instrumental errors$ 101. $A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope ?$ (1) $0.001 cm$ (2) $0.002 mm$ (3) $0.002 cm$ (4) $0.005 cm$ 102. $In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 \times 10^{- 12} m the minimum electron energy required is close to:$ (1) $500 keV$ (2) $100 keV$ (3) $l keV$ (4) $25 keV$ 103. $In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is____mm. [Assume least count is 0.01 mm]$ (1) $1.50$ (2) $1.48$ (3) $1.54$ (4) $1.51$ 104. $In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is____mm.$ (1) $0.005$ (2) $0.05$ (3) $0.002$ (4) $0.02$ 105. $The dimension of \frac{1}{2} ϵ_{0} E^{2}, where s_{0} is permitvity of free space and E is electric field, is$ (1) $M L^{2} T^{- 2}$ (2) $M L^{- 1} T^{- 2}$ (3) $M L^{2} T^{- 1}$ (4) $ML T^{- 1}$ 106. $Electrical as well as gravitational effects can be thought to be caused by fields. Which of the following is true for an electrical or gravitational field?$ (1) $Fields are useful for understanding forces acting through distance.$ (2) $The field concept is often used to describe contact forces.$ (3) $There is no way to verify the existence of a force field since it is just a concept.$ (4) $Gravitational or electric field does not exist in the space around an object.$ 107. $The dimensions of impulse are equal to that of$ (1) $pressure$ (2) $linear momentum$ (3) $force$ (4) $angular momentum$ 108. $A vernier callipers has 20 divisions on the vernier scale, which coincides with 19^{th} division on the main scale. The least count of the instrument is 0.1 mm . One main scale division is equal to _____mm .$ (1) $0.5$ (2) $2$ (3) $5$ (4) $1$ 109. $The ratio of dimensions of Planck's constant to that of moment of inertia is the dimensions of$ (1) $angular momentum$ (2) $velocity$ (3) $frequency$ (4) $time$ 110. $Given below are two statements : Statement I: Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statement II: Au < Parsec (Pc) < ly In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $Both Statements I and Statements II are incorrect$ (2) $Statements I is correct but Statements II is incorrect$ (3) $Both Statements I and Statements II are correct$ (4) $Statements I is incorrect but Statements II is correct$ 111. $Consider a series of measurements of the length of a box in an experiment. The readings are 2.4 m, 2.5 m, 2.6 m, 2.8 m, 3.0 m . What would be the relative error?$ (1) $0.110$ (2) $0.089$ (3) $0.079$ (4) $0.072$ 112. $While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is \frac{x}{50} mm . The value of x is:$ (1) $21$ (2) $142$ (3) $71$ (4) $42$ 113. $If e is the electronic charged, c is the speed of light in free space and h is planck's constant, the quantity \frac{1}{4 π ϵ _{0}} \frac{\| e \| ^{2}}{hc} has dimensions of :$ (1) $(LC^{- 1})$ (2) $(M^{0} L^{0} T^{0})$ (3) $(ML T^{0})$ (4) $(ML T^{- 1})$ 114. $Match List - I with List- II List I: (A) h (Planck’s constant) (B) E (kinetic energy) (C) V (electric potential) (D) P (linear momentum) List II: (I) M L T^{- 1} (II) M L^{2} T^{- 1} (III) M L^{2} T^{- 2} (IV) M L^{2} I^{- 1} T^{- 3} Choose the correct answer from the options given below:$ (1) $(A) \to (II), (B) \to (III), (C) \to (IV), (D) \to (I)$ (2) $(A) \to (I), (B) \to (II), (C) \to (IV), (D) \to (III)$ (3) $(A) \to (III), (B) \to (II), (C) \to (IV), (D) \to (I)$ (4) $(A) \to (III), (B) \to (IV), (C) \to (II), (D) \to (I)$ 115. $The strongest force among the following forces in nature is$ (1) $electromagnetic force$ (2) $weak nuclear force$ (3) $gravitational force$ (4) $strong nuclear force$ 116. $Assertion A: If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5mm and there are 50 total divisions on circular scale, then least count is 0.001cm. Reason R: Least Count = \frac{Pitch}{Total divisions on circular scale} choose the most appropriate answer from the options given below:$ (1) $A is not correct but R is correct.$ (2) $Both A and R are correct and R is the correct explanation of A.$ (3) $A is correct but R is not correct.$ (4) $Both A and R are correct and R is NOT the correct explanation of A.$ 117. $If E and E_{0} represent the energies, t and t_{0} represent the times, then which of the following is dimensionally correct relation?$ (1) $E = E_{0} e^{- t}$ (2) $E = E_{0} t_{0} e^{- t / t_{0}}$ (3) $E = E_{0} t_{0} e^{- t^{2}}$ (4) $E = E_{0} e^{- t / t_{0}}$ 118. $In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of M^{P} L^{Q} T^{R} A^{S}, where value of ' Q' and ' R' are$ (1) $(3, - 5)$ (2) $(- 2, 1)$ (3) $(- 2, 2)$ (4) $(1, - 1)$ 119. $A physical quantity Q is related to four observables a, b, c, d as follows : Q = \frac{ab ^{4}}{cd} where, a (60 \pm 3) Pa; b = (20 \pm 0.1) m; c = (40 \pm 0.2) Nsm^{- 2} and d = (50 \pm 0.1) m, then the percentage error in Q is \frac{x}{1000}, where x = .$ 120. $In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division.Then the value of vernier constant will be.............. x 1 0^{- 2} mm$