Units, Dimensions & Measurements PYQs Set 2 (PDF)

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Set 2 of 10 · Questions 31-60 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 2 (Q31-60)
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31. $In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4^{th} division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?$ (1) $10$ (2) $5$ (3) $20$ (4) $40$ 32. $In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of (M^{P} L^{Q} T^{R} A^{S}) . The value of P and Q are:$ (1) $- 1, 0$ (2) $0, - 1$ (3) $- 1, 1$ (4) $1, - 1$ 33. $If ϵ, E and t represent the free space permittivity, electric field and time respectively, then the unit of \frac{ϵ E}{t} will be :$ (1) $Am^{2}$ (2) $Am$ (3) $A / m^{2}$ (4) $A / m$ 34. $A metal wire has mass (0.4 \pm 0.002) g, radius (0.3 \pm 0.001) mm and length (5 0.02) cm . The maximum possible percentage error in the measurement of density will nearly be [NEET 2023]$ (1) $1.3 %$ (2) $1.6 % .$ (3) $1.4 % .$ (4) $1.2 %$ 35. $A force is defined by F = α t^{2} + βt acts on a particle at a given time t . The factor which is dimensionless, if α and β are constants, is [NEET 2024]$ (1) $\frac{βt}{α}$ (2) $\frac{αt}{β}$ (3) $αβt$ (4) $\frac{αβ}{t}$ 36. $If C be the capacitance and V be the electric potential, then the dimensional formula of C V^{2} is$ (1) $M^{1} L^{2} T^{- 2} A^{0}$ (2) $M^{0} L^{1} T^{- 2} A^{0}$ (3) $M^{1} L^{1} T^{- 2} A^{- 1}$ (4) $M^{1} L^{- 3} T^{1} A^{- 1}$ 37. $Due to an explosion underneath water, a bubble started oscillating. If this oscillation has time period T, which is proportional to p^{a} S^{b} E^{g}, where p is static pressure, S is density of water and E is total energy of explosion. Determine a, b and g .$ (1) $α = - \frac{3}{2}, β = \frac{1}{3}, γ = - \frac{5}{6}$ (2) $α = - \frac{5}{6}, β = \frac{1}{2}, γ = \frac{1}{3}$ (3) $α = \frac{1}{2}, β = - \frac{5}{6}, γ = \frac{7}{4}$ (4) $α = \frac{1}{3}, β = \frac{3}{2}, γ = \frac{4}{3}$ 38. $Length of a simple pendulum is 25.0 cm and time of 40 oscillation is 50 sec . If resolution of stop watch is 1 sec then accuracy is g is (in %)$ (1) $2.4$ (2) $3.4$ (3) $4.4$ (4) $5.4$ 39. $Dimensional formula of self-inductance is$ (1) $[ML T^{- 2} A^{- 2}]$ (2) $[M L^{2} T^{- 1} A^{- 2}]$ (3) $[M L^{2} T^{- 2} A^{- 2}]$ (4) $[M L^{2} T^{- 2} A^{- 1}]$ 40. $Which two of the following five physical parameters have the same dimensions?1. energy density 2. refractive index 3. dielectric constant 4. Young’s modulus 5. magnetic field$ (1) $1 and 4$ (2) $1 and 5$ (3) $2 and 4$ (4) $3 and 5$ 41. $The dimension of \frac{1}{2} ϵ_{0} E^{2}, where ϵ_{0} is permittivity of free space and E is electric field, is$ (1) $ML^{2} T^{- 2}$ (2) $ML^{- 1} T^{- 2}$ (3) $ML^{2} T^{- 1}$ (4) $MLT^{- 1}$ 42. $The density of a material in SI unit of is 128 kg m^{- 3} certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is:$ (1) $40$ (2) $16$ (3) $640$ (4) $410$ 43. $The dimensions of the ratio of magnetic flux (φ) and permeability (μ) are$ (1) $(M^{0} L^{1} T^{0} A^{1})$ (2) $(M^{0} L^{- 3} T^{0} A^{1})$ (3) $(M^{0} L^{1} T^{1} A^{- 1})$ (4) $(M^{0} L^{2} T^{0} A^{1})$ 44. $Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length? [NEET 2016]$ (1) $\frac{hG}{c ^{3/2}}$ (2) $\frac{hG}{c ^{5/2}}$ (3) $\frac{hc}{G}$ (4) $\frac{Gc}{h ^{3/2}}$ 45. $The SI unit of length is 'metre'. Suppose we adopt a new unit of length which equals x metre. Then, the area of 1 m^{2} expressed in terms of new unit has a magnitude$ (1) $x$ (2) $x^{2}$ (3) $\frac{1}{x}$ (4) $\frac{1}{x ^{2}}$ 46. $If the dimensional formula of '(Energy \times speed)' is (M^{a} L^{b} T^{c})] then a, b and c are$ (1) $(1, 3, - 3)$ (2) $(1, 2, 2)$ (3) $(1, 2, 3)$ (4) $(1, 3, - 2)$ 47. $(ML^{2} T^{- 2} K^{- 1}) is the dimensional formula of the physical quantity$ (1) $Boltzmann constant$ (2) $Specific heat capacity$ (3) $Thermal expansion coefficient$ (4) $Latent heat$ 48. $Match List - I with List - II. List I: (A) Permeability of free space (B) Magnetic field (C) Magnetic moment (D) Torsional constant List II: (I) M L^{2} T^{- 2} (II) M T^{- 2} A^{- 1} (III) M L T^{- 2} A^{- 2} (IV) L^{2} A Choose the correct answer from the options given below :$ (1) $(A)-(IV), (B)-(III), (C)-(I), (D)-(II)$ (2) $(A)-(III), (B)-(II), (C)-(IV), (D)-(I)$ (3) $(A)-(I), (B)-(IV), (C)-(II), (D)-(III)$ (4) $(A)-(II), (B)-(I), (C)-(III), (D)-(IV)$ 49. $Turpentine oil is flowing through a tube of length l and radius r . The pressure difference between the two ends of the tube is P . The viscosity of oil is given by η = \frac{P ( r ^{2} - x ^{2} )}{4 vl} where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of η are$ (1) $[MLT]$ (2) $[ML T^{- 1}]$ (3) $[M L^{2} T^{- 2}]$ (4) $[M L^{- 1} T^{- 1}]$ 50. $The dimension of \frac{μ _{0}}{ϵ _{0}} is equal to that of: (μ_{0} = Vacuum permeability and ϵ_{0} = Vacuum permittivity)$ (1) $Voltage$ (2) $Inductance$ (3) $Resistance$ (4) $Capacitance$ 51. $A quantity Q is formulated as . X , Y , and Z are independent parameters which have fractional errors of , and 0.5 , respectively in measurement. The maximum fractional error of is$ (1) $0.6$ (2) $0.8$ (3) $0.7$ (4) $0.1$ 52. $The dimensions of s b^{4}, where s is Stefan's constant and b is Wien's constant are$ (1) $(M^{0} L^{0} T^{0})$ (2) $(M L^{4} T^{- 3})$ (3) $(M L^{- 2} T)$ (4) $(M L^{6} T^{- 3})$ 53. $The ratio of the dimensions of Planck’s constant and that of moment of inertia is the dimensions of$ (1) $time$ (2) $frequency$ (3) $angular momentum$ (4) $velocity$ 54. $If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be$ (1) $FA^{- 1} V^{0}$ (2) $FA^{2} V^{- 1}$ (3) $FA^{2} V^{- 2}$ (4) $FA^{2} V^{- 3}$ 55. $A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is [NEET 2020]$ (1) $0.25 mm$ (2) $0.5 mm$ (3) $1.0 mm$ (4) $0.01 mm$ 56. $If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are$ (1) $[FV T^{- 1}]$ (2) $FV T^{- 2}]$ (3) $[F V^{- 1} T^{- 1}]$ (4) $[F V^{- 1} T]$ 57. $A calorie is a unit of heat energy and its value is 4.18 J, where 1 J = 1 kg m^{2} s^{- 2} . Suppose we use a new system of units in which unit of mass equals x kg, the unit of length equals y m and the unit of the time is z sec . Then the value of a calorie in the new system of units is$ (1) $4.18 \frac{z ^{2}}{x y ^{2}}$ (2) $4.18 \frac{x y ^{2}}{z ^{2}}$ (3) $4.18 \frac{z ^{2}}{x}$ (4) $4.18 \frac{y ^{2}}{x z ^{2}}$ 58. $In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1 %, 2 %, 3 % and 4 %, respectively. Then, the maximum percentage of error in the measurement X, where X = \frac{A ^{2} B ^{1/2}}{C ^{1/3} D ^{3}}, will be [NEET 2019]$ (1) $10%$ (2) $(3/13) %$ (3) $16%$ (4) $- 10 %$ 59. $If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as (η^{x} ρ^{y} r^{z}) where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by$ (1) $1, - 1, - 1$ (2) $- 1, - 1, 1$ (3) $- 1, - 1, - 1$ (4) $1, 1, 1$ 60. $A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is \frac{x}{121} . The value of x is___$