Units, Dimensions & Measurements PYQs Set 8 (PDF)

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Mere Teacher · Previous Year Questions NEET Physics · Units, Dimensions & Measurements · Set 8 (Q211-240)
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211. $A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e ^{2}}{4 π \in _{0}} is [c is velocity of light, G is universal constant of gravitation and e is charge] :$ (1) $\frac{1}{c ^{2}} [G \frac{e ^{2}}{4 π ϵ _{0}}]^{1/2}$ (2) $c^{2}$ (3) $\frac{1}{c ^{2}} [\frac{e ^{2}}{G 4 π ϵ _{0}}]^{1/2}$ (4) $\frac{1}{c} G \frac{e ^{2}}{4 π \in _{0}}$ 212. $The speed of a wave produced in water is given by v = λ^{a} g^{b} ρ^{c} . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are$ (1) $1, - 1, 0$ (2) $\frac{1}{2}, 0, \frac{1}{2}$ (3) $1, 1, 0$ (4) $\frac{1}{2}, \frac{1}{2}, 0$ 213. $If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is$ (1) $86.4s$ (2) $4.32s$ (3) $43.2s$ (4) $8.64s$ 214. $If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t,v and l is :$ (1) $t^{- 1} v^{1} l^{- 2}$ (2) $t^{1} v^{2} l^{- 1}$ (3) $t^{- 2} v^{- 1} l^{1}$ (4) $t^{- 1} v^{- 2} l^{1}$ 215. $Which of the following is not a dimensionless quantity?$ (1) $Relative magnetic permeability (_{r}^{μ})$ (2) $Power factor$ (3) $Permeability of free space (_{0}^{μ})$ (4) $Quality factor$ 216. $The magnitude of vectors O A, O B and O C in the given figure are equal. The direction of O A + O B - O C with -axis will be :-$ (1) $tan^{- 1} \frac{( 1 - 3 - 2 )}{( 1 + 3 + 2 )}$ (2) $tan^{- 1} \frac{( 3 - 1 + 2 )}{( 1 + 3 - 2 )}$ (3) $tan^{- 1} \frac{( 3 - 1 + 2 )}{( 1 - 3 + 2 )}$ (4) $tan^{- 1} \frac{( 1 + 3 - 2 )}{( 1 - 3 - 2 )}$ 217. $In an experiment, the percentage of error occurred in the in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = \frac{A ^{2} B ^{1/2}}{C ^{1/3} D ^{3}}, will be$ (1) $10 %$ (2) $(\frac{3}{13}) %$ (3) $16%$ (4) $- 10%$ 218. $Match List I with List II List-I (A) Spring constant (I) [T^{- 1}] (C) Angular momentum (III) [M L^{2}] List-II (B) Angular speed (II) [M T^{- 2}] (D) Moment of Inertia (IV) [M L^{2} T^{- l}] Choose the correct answer from the options given below:$ (1) $A-I, B-III, C-II, D-IV$ (2) $A-IV,B-I, C-III, D-II$ (3) $A-II, B-I, C-IV, D-III$ (4) $A-II, B-III, C-I, D-IV$ 219. $Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density is constant. The velocity v of any point on the surface of the expanding sphere is proportional to$ (1) $R^{3}$ (2) $R$ (3) $R^{2/3}$ (4) $\frac{1}{R}$ 220. $In an experiment to find out the diameter of wire using screw gauge, the following observation were (A) Screw moves 0.5 mm on main scale in one complete rotation (B) Total divisions on circular scale = 50 (C) Main scale reading is 2.5 mm (D) 4 5^{t h} division of circular scale is in the pitch line (E) Instrument has 0.03 mm negative error Then the diameter of wire is :$ (1) $2.92 mm$ (2) $2.54 mm$ (3) $2.98 mm$ (4) $3.45 mm$ 221. $If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :$ (1) $[F L^{- 4} T^{2}]$ (2) $[F L^{- 3} T^{2}]$ (3) $[F L^{- 5} T^{2}]$ (4) $[F L^{- 3} T^{3}]$ 222. $If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:$ (1) $[h^{1/2} c^{- 1/2} G^{1}]$ (2) $[h^{1} c^{1} G^{- 1}]$ (3) $[h^{- 1/2} c^{1/2} G^{1/2}]$ (4) $[h^{1/2} c^{1/2} G^{- 1/2}]$ 223. $List I A. Young’s Modulus (Y) B. Co-efficient of Viscosity (η) C. Planck’s Constant (h) D. Work Function (ϕ) List II I. [M L^{- 1} T^{- 1}] II. [M L^{2} T^{- 1}] III. [M L^{- 1} T^{- 2}] IV. [M L^{2} T^{- 2}] Choose the correct answer from the options given below:$ (1) $A-II, B-III, C-IV, D-I$ (2) $A-III, B-I, C-II, D-IV$ (3) $A-I,B-III, C-IV,D-II$ (4) $A-I,B-II,C-III,D-IV$ 224. $The equation of a circle is given by x^{2} + y^{2} = a^{2}, where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : (x - A t)^{2} + (y - \frac{t}{B})^{2} = a^{2} . The dimensions of t is given as [T^{- 1}] .$ (1) $A = [L^{- 1} T],B=[L T^{- 1}]$ (2) $A = (LT],B = [L^{- l} T^{- 1}]$ (3) $A = [L^{- l} T^{- 1}],B = [L T^{- 1}]$ (4) $A = [L^{- 1} T^{- 1}],B = [LT]$ 225. $Which of the following units denotes the dimensions M L^{2} / Q^{2}, where Q denotes the electric charge?$ (1) $H/ m^{2}$ (2) $Weber (Wb)$ (3) $Wb/ m^{2}$ (4) $Henry (H)$ 226. $Dimension of \frac{1}{μ _{0} ϵ _{0}} should be equal to$ (1) $L T^{- 1}$ (2) $T^{2} L^{- 2}$ (3) $L^{2} T^{- 2}$ (4) $T L^{- 1}$ 227. $If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :$ (1) $[P A^{- 1} T°]$ (2) $[P A T^{- 1}]$ (3) $[P A^{- 1} T]$ (4) $[P A^{- 1} T^{- 1}]$ 228. $Match List I with List II LIST I A. Planck’s constant (h) B. Stopping potential (Vs) C. Work function (^{φ}) D. Momentum (p) LIST II I. [M^{1} L^{2} T^{- 2}] II. [M^{1} L^{1} T^{- 1}] III. [M^{1} L^{2} T^{- 1}] IV [M^{1} L^{2} T^{- 3} A^{- 1}]$ (1) $A-III,B-I, C-II,D-IV$ (2) $A-III, B-IV, C-I, D-II$ (3) $A-II, B-IV, C-III, D-I$ (4) $A-I, B-III, C-IV, D-II$ 229. $The density of a material in SI units is 128 k g m^{-3} . In certain units in which the units of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is :$ (1) $410$ (2) $40$ (3) $640$ (4) $16$ 230. $Match List Ι with List ΙΙ and select the correct answer using the codes given below the lists : List Ι List ΙΙ P. Boltzmann constant 1. [M L^{2} T^{-1}] Q. Coefficient of viscosity 2. [M L^{-1} T^{-1}] R. Planck constant 3. [M L T^{-3} K^{-1}] S. Thermal conductivity 4. [M L^{2} T^{-2} K^{-1}] Codes : P Q R S$ (1) $3 1 2 4$ (2) $3 2 1 4$ (3) $4 2 1 3$ (4) $4 1 2 3$ 231. $If A = 3 i - 2 j + k, B = i - 3 j + 5 k and C = 2 i + j - 4 k form a right angled triangle. Then out of the following which one is satisfied?$ (1) $A=B+C and A^{2} = B^{2} + C^{2}$ (2) $A=B+C and B^{2} = A^{2} + C^{2}$ (3) $B=A+C and B^{2} = A^{2} + C^{2}$ (4) $B=A+C and A^{2} = B^{2} + C^{2}$ 232. $Match List I with List II List-I A. Surface tension B. Pressure C. Viscosity D. Impulse List-II I. Kg m^{- 1} s^{- 1} II. Kg m s^{- 1} III. Kg m^{- 1} s^{- 2} IV. Kg s^{- 2} Choose the correct answer from the options given below:$ (1) $A-IV, B-III,C-II, D-I$ (2) $A-IV, B-III, C-I, D-II$ (3) $A-III, B-IV, C-I, D-II$ (4) $A-II, B-I, C-III, D-IV$ 233. $Velocities (V) and accelerations (a) in two systems of units 1 and 2 are related as V_{2} = \frac{n}{m ^{2}} V_{1} and a_{2} = \frac{a _{1}}{mn} respectively. Here m and n are constants. Dimensionally relations between distances (S_{1} and S_{2}) and times (t_{1} and t_{2}) in the two systems are respectively.$ (1) $S_{2} = (\frac{n}{m})^{3} S_{1} and t_{2} = \frac{n ^{2}}{m} t_{1}$ (2) $S_{2} = (\frac{n}{m})^{3} S_{1} and t_{2} = \frac{m}{n ^{2}} t_{1}$ (3) $S_{2} = \frac{m}{n ^{2}} S_{1} and t_{2} = \frac{m ^{2}}{n ^{4}} t_{1}$ (4) $S_{2} = \frac{n ^{2}}{m} S_{1} and t_{2} = \frac{m ^{2}}{n ^{4}} t_{1}$ 234. $If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as [η^{x} ρ^{y} r^{z}] where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively then the values of x, y and z are given by$ (1) $- 1, - 1, - 1$ (2) $1, 1, 1$ (3) $1, - 1, - 1$ 235. $Two protons are kept at a separation of 40Å . F_{n} is the nuclear force and F_{e} is the electrostatic force between them. Then$ (1) $F_{n} ≪ F_{e}$ (2) $F_{n} \approx F_{e}$ (3) $F_{n} ≫ F_{e}$ (4) $F_{n} = F_{e}$ 236. $The quantities x = \frac{1}{μ _{0} ϵ _{0}}, y = \frac{E}{B} and z = \frac{l}{C R} are defined where C -capacitance, R -Resistance, l length, E -Electric field, B -magnetic field and ϵ_{0}, μ_{0} - free space permittivity and permeability respectively. Then$ (1) $Only x and y have the same dimension$ (2) $Only x and z have the same dimension$ (3) $x, y and z have the same dimension$ (4) $Only y and z have the same dimension$ 237. $The dimensions of (μ_{0} ϵ_{0})^{- 1/2} are$ (1) $[L^{1/2} T^{- 1/2}]$ (2) $[L2T]$ (3) $[L T^{- 1}]$ (4) $[L^{1/2} T^{1/2}]$ 238. $Dimensions of gyromagnetic ratio are$ (1) $(L^{1} M^{0} T^{1} I^{1})$ (2) $(L^{1} M^{0} I^{0} T^{- 1})$ (3) $(L^{0} M^{- 1} T^{1} I^{1})$ (4) $(L^{- 1} M^{0} T^{1} I^{1})$ 239. $The dimensional formula of torque is$ (1) $[M L^{2} T^{- 2}]$ (2) $[ML T^{- 2}]$ (3) $[M L^{- 1} T^{- 2}]$ (4) $[M L^{- 2} T^{- 2}]$ 240. $Dimensions of stress are [NEET 2020]$ (1) $M L^{2} T^{- 2}$ (2) $M L^{0} T^{- 2}$ (3) $M L^{- 1} T^{- 2}$ (4) $M L T^{- 2}$