Units, Dimensions & Measurements PYQs Set 1 (PDF)

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 1 (Q1-30)
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1. $A certain vector in the yz plane has a y -component of 12 m and a z -component of 8 m . It is then rotated in the yz plane so that its y -component is halved. Then its new z -component is approximately$ (1) $14 m$ (2) $13.11 m$ (3) $10 m$ (4) $2.0 m$ 2. $The dimensions of torque are same as that of$ (1) $moment of force$ (2) $pressure$ (3) $acceleration$ (4) $impulse$ 3. $Match List-I with List-II. List-I (A) Torque (B) Impulse (C) Tension (D) Surface Tension List-II (I) M L T^{- 1} (II) M T^{- 2} (III) M L^{2} T^{- 2} (IV) M L T^{- 2} Choose the most appropriate answer from the option given below :$ (1) $(A)-(III), (B)-(I), (C)-(IV), D-(II)$ (2) $(A)-(II), (B) -(IV), (D)-(III)$ (3) $(A)-(I), (B)-(III), (C)-(IV), (D)-(II)$ (4) $(A)-(III), (B)-(IV), (C) -(I), (D)-(II)$ 4. $What is the dimension of \frac{1}{μ _{0} ϵ _{0}} ? (μ_{0} = magnetic permeability and ϵ_{0} = permittivity of free space)$ (1) $(L^{2} T^{- 2})$ (2) $(LT^{- 1})$ (3) $(L^{2} T^{2})$ (4) $(LT^{2})$ 5. $Which of the following pairs has same dimensions?$ (1) $Current density and charge density$ (2) $Angular momentum and linear momentum$ (3) $Spring constant and surface energy$ (4) $Force and torque$ 6. $Match List-I with List-II. List-I A. Angular momentum B. Torque C. Stress D. Pressure gradient List-II I. [M L^{2} T^{- 2}] II. [M L^{- 2} T^{- 2}] III. [M L^{2} T^{- 1}] IV. [M L^{- l} T^{- 2}] Choose the correct answer from the options given below:$ (1) $A-I, B-IV, C-III, D-II$ (2) $A-III,B-I,C-IV,D-II$ (3) $A-II,B-III,C-IV,D-I$ (4) $A-IV, B-II, C-I, D-III$ 7. $If and represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :$ (1) $ohm$ (2) $mho$ (3) $joule$ (4) $newton$ 8. $An equation is given here (P + \frac{a}{V ^{2}}) = b \frac{Θ}{V} where P = Pressure, V = Volume and Θ = Absolute temperature. If a and b are constants, the dimensions of a will be$ (1) $[M L^{- 5} T^{- 1}]$ (2) $[M L^{5} T^{1}]$ (3) $[M L^{5} T^{- 2}]$ (4) $[M^{- 1} L^{5} T^{2}]$ 9. $Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) isproportional to:$ (1) $\frac{hc ^{5}}{G}$ (2) $\frac{c ^{3}}{Gh}$ (3) $\frac{Gh}{c ^{5}}$ (4) $\frac{Gh}{c ^{3}}$ 10. $The electric flux is φ = ασ + βλ where λ and σ are linear and surface charge density, respectively. (\frac{α}{β}) represents$ (1) $electric field$ (2) $area$ (3) $charge$ (4) $displacement$ 11. $If 50 Vernier divisions are equal to 49 main scal divisions of a travelling microscope and on smallest reading of main scale is 0.5 mm, th Vernier constant of travelling microscope is:$ (1) $0.1 mm$ (2) $0.1 cm$ (3) $0.01 cm$ (4) $0.01 mm$ 12. $The pair of quantities having same dimensions is$ (1) $Impulse and Surface Tension$ (2) $Angular momentum and Work$ (3) $Work and Torque$ (4) $Young’s modulus and Energy$ 13. $10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :$ (1) $\frac{1}{2}$ (2) $\frac{10}{11}$ (3) $\frac{50}{11}$ (4) $\frac{5}{11}$ 14. $A force between two protons is same as the force between proton and neutron. The nature of the force is$ (1) $electrical force$ (2) $weak nuclear force$ (3) $gravitational force$ (4) $strong nuclear force.$ 15. $A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of - 0.004 cm, the correct diameter of the ball is$ (1) $0.521 cm$ (2) $0.525 cm$ (3) $0.053 cm$ (4) $0.529 cm$ 16. $The dimensions (MLT^{- 2} A^{- 2})] belong to the [NEET 2022]$ (1) $magnetic flux$ (2) $self-inductance$ (3) $magnetic permeability$ (4) $electric permittivity$ 17. $Match List - I with List - II. List I: (A) Angular Impulse (B) Latent Heat (C) Electrical resistivity (D) Electromotive force List II: (I) M^{0} L^{2} T^{- 2} (II) M L^{2} T^{- 3} A^{- 1} (III) M L^{2} T^{- 1} (IV) M L^{3} T^{- 3} A^{- 2}$ (1) $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$ (2) $(A)-(I), (B)-(III), (C)-(IV), (D)-(II)$ (3) $(A)-(III), (B)-(I), (C)-(II), (D)-(IV)$ (4) $(A)-(III), (B)-(I), (C)-(IV), (D)-(II)$ 18. $The pair of physical quantities not having same dimensions is :$ (1) $Pressure and Young's modulus$ (2) $Surface tension and impulse$ (3) $Torque and energy$ (4) $Angular momentum and Planck's constant$ 19. $Given a charge q, current I and permeability of vacuum μ_{o^{*}} . Which of the following quantity has the dimension of momentum?$ (1) $qI / μ_{o}$ (2) $q^{2} μ_{o} I$ (3) $q μ_{0} / I$ (4) $q μ_{o} I$ 20. $The dimensional formula of magnetic flux is$ (1) $[M^{0} L^{- 2} T^{- 2} A^{- 2}]$ (2) $[M L^{0} T^{- 2} A^{- 2}]$ (3) $[M L^{2} T^{- 2} A^{- 1}]$ (4) $[M L^{2} T^{- 1} A^{3}]$ 21. $The dimensions of Planck’s constant equals to that of$ (1) $energy$ (2) $momentum$ (3) $angular momentum$ (4) $power$ 22. $The angle of 1 (minute of arc) in radian is nearly equal to [NEET 2020]$ (1) $2.91 \times 10^{- 4} rad$ (2) $4.85 \times 10^{- 4} rad$ (3) $4.80 \times 10^{- 6} rad$ (4) $1.75 \times 10^{- 2} rad$ 23. $A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm; 5.65 mm} . The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm . The average diameter of the pencil should therefore be recorded as$ (1) $(5.5375 \pm 0.0739) mm$ (2) $(5.54 \pm 0.07) mm$ (3) $(5.538 \pm 0.074) mm$ (4) $(5.5375 \pm 0.0740) mm$ 24. $A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of:$ (1) $15%$ (2) $25%$ (3) $75%$ (4) $5%$ 25. $In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm . The expected least count of the instrument used in recording these readings is____mm.$ (1) $0.001$ (2) $0.1$ (3) $0.01$ (4) $0.05$ 26. $Plane angle and solid angle have [NEET 2022]$ (1) $Dimensions but no units$ (2) $No units and no dimensions$ (3) $Both units and dimensions$ (4) $Units but no dimensions$ 27. $The ratio of relative strengths of the gravitational force and the electromagnetic force between two charged particles is$ (1) $10^{- 11}$ (2) $10^{- 39}$ (3) $10^{- 37}$ (4) $10^{- 41}$ 28. $The unit of thermal conductivity is [NEET 2019]$ (1) $Jm^{- 1} K^{- 1}$ (2) $Wm K^{- 1}$ (3) $W m^{- 1} K^{- 1}$ (4) $Jm K^{- 1}$ 29. $Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :$ (1) $205.3 m$ (2) $205.333 m$ (3) $205.33 m$ (4) $205 m$ 30. $If the screw on a screw-gauge is given six rotations, it moves by 3mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :$ (1) $0.01 cm$ (2) $0.02 mm$ (3) $0.001 mm$ (4) $0.001 cm$