Units, Dimensions & Measurements PYQs Set 8 (PDF)

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Set 8 of 10 · Questions 211-240 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 8 (Q211-240)
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211. $Match List I with List II List-I (A) Torque (I) M L^{- 2} T^{- 2} (C) Pressure gradient (III) M L^{- 1} T^{- 1} List-II (B) Stress (II) M L^{2} T^{- 2} (D) Coefficient of viscosity (IV) M L^{- 1} T^{- 2} Choose the correct answer from the options given below :$ (1) $A-II, B-I, C-IV, D-III$ (2) $A-IV, B-II, C-III, D-I$ (3) $A-II, B-IV, C-I, D-III$ (4) $A-III, B-IV, C-I, D-II$ 212. $Which of the following has the dimensions of pressure?$ (1) $[ML T^{- 2}]$ (2) $[M L^{- 1} T^{- 2}]$ (3) $[M L^{- 2} T^{- 2}]$ (4) $[M^{- 1} L^{- 1}]$ 213. $The maximum percentage error in the measurment of density of a wire is [Given, mass of wire = (0.60 \pm 0.003) g radius of wire = (0.50 \pm 0.01) cm length of wire = (10.00 \pm 0.05) cm]$ (1) $8$ (2) $5$ (3) $4$ (4) $7$ 214. $If E and E_{0} denote energies at time t and t0 respectively, and L and L_{0} distance from some point at t and t0 respectively, then which of the following equations can be declared to be incorrect on dimensional grounds.(A) E = \frac{2 E _{0} L}{L _{0} - L} (B) E = E_{0} e^{- 2 L / L_{0}} (C) E = 2 L e^{L_{0}} - L / E_{0} (D) E = 2 (E_{0} / L_{0}) \times e^{- L / L_{0}}$ (1) $A, B only$ (2) $A, C only$ (3) $A, C, D only$ (4) $C, D only$ 215. $In a vernier callipers, (N + 1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is: [NEET 2024]$ (1) $\frac{1}{10 N}$ (2) $\frac{1}{100 ( N + 1 )}$ (3) $100 N$ (4) $10 (N + 1)$ 216. $A physical quantity Q is found to depend on observables x, y and z, obeying relation Q = \frac{x ^{3} y ^{2}}{z} . The percentage error in the measurements of x, y and z are 1 %, 2 % and 4 % respectively. What is percentage error in the quantity Q ?$ (1) $11 %$ (2) $4 %$ (3) $1 %$ (4) $3 %$ 217. $One main scale division of a vernier caliper is equal to m units. If n^{th} division of main scale coincides with (n + 1)^{th} division of vernier scale, the least count of the vernier caliper is :$ (1) $\frac{n}{( n + 1 )}$ (2) $\frac{1}{( n + 1 )}$ (3) $\frac{m}{( n + 1 )}$ (4) $\frac{m}{n ( n + 1 )}$ 218. $The physical quantity having the dimensions (M^{- 1} L^{- 3} T^{3} A^{2}) is$ (1) $resistance$ (2) $resistivity$ (3) $electrical conductivity$ (4) $electromotive force.$ 219. $If E,L,M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P= E L^{2} M^{- 5} G^{- 2} are :-$ (1) $[M^{0} L^{1} T^{0}]$ (2) $[M^{- 1} L^{- 1} T^{2}]$ (3) $[M^{1} L^{1} T^{- 2}]$ (4) $[M^{0} L^{0} T^{0}]$ 220. $An expression for a dimensionless quantity P is given by P = \frac{α}{β} lo g_{e} (\frac{k t}{β x}); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be :$ (1) $[M° L^{- 1} T°]$ (2) $[ML° T^{- 2}]$ (3) $[M L T^{- 2}]$ (4) $[M L^{2} T^{- 2}]$ 221. $A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e ^{2}}{4 π \in _{0}} is [c is velocity of light, G is universal constant of gravitation and e is charge] :$ (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) $\frac{1}{c} G \frac{e ^{2}}{4 π \in _{0}}$ 222. $The speed of a wave produced in water is given by v = λ^{a} g^{b} ρ^{c} . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are$ (1) $1, - 1, 0$ (2) $\frac{1}{2}, 0, \frac{1}{2}$ (3) $1, 1, 0$ (4) $\frac{1}{2}, \frac{1}{2}, 0$ 223. $If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is$ (1) $86.4s$ (2) $4.32s$ (3) $43.2s$ (4) $8.64s$ 224. $If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t,v and l is :$ (1) $t^{- 1} v^{1} l^{- 2}$ (2) $t^{1} v^{2} l^{- 1}$ (3) $t^{- 2} v^{- 1} l^{1}$ (4) $t^{- 1} v^{- 2} l^{1}$ 225. $Which of the following is not a dimensionless quantity?$ (1) $Relative magnetic permeability (_{r}^{μ})$ (2) $Power factor$ (3) $Permeability of free space (_{0}^{μ})$ (4) $Quality factor$ 226. $The magnitude of vectors O A, O B and O C in the given figure are equal. The direction of O A + O B - O C with -axis will be :-$ (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) $tan^{- 1} \frac{( 1 + 3 - 2 )}{( 1 - 3 - 2 )}$ 227. $In an experiment, the percentage of error occurred in the in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = \frac{A ^{2} B ^{1/2}}{C ^{1/3} D ^{3}}, will be$ (1) $10 %$ (2) $(\frac{3}{13}) %$ (3) $16%$ (4) $- 10%$ 228. $Match List I with List II List-I (A) Spring constant (I) [T^{- 1}] (C) Angular momentum (III) [M L^{2}] List-II (B) Angular speed (II) [M T^{- 2}] (D) Moment of Inertia (IV) [M L^{2} T^{- l}] Choose the correct answer from the options given below:$ (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) $A-II, B-III, C-I, D-IV$ 229. $Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density is constant. The velocity v of any point on the surface of the expanding sphere is proportional to$ (1) $R^{3}$ (2) $R$ (3) $R^{2/3}$ (4) $\frac{1}{R}$ 230. $In an experiment to find out the diameter of wire using screw gauge, the following observation were (A) Screw moves 0.5 mm on main scale in one complete rotation (B) Total divisions on circular scale = 50 (C) Main scale reading is 2.5 mm (D) 4 5^{t h} division of circular scale is in the pitch line (E) Instrument has 0.03 mm negative error Then the diameter of wire is :$ (1) $2.92 mm$ (2) $2.54 mm$ (3) $2.98 mm$ (4) $3.45 mm$ 231. $If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :$ (1) $[F L^{- 4} T^{2}]$ (2) $[F L^{- 3} T^{2}]$ (3) $[F L^{- 5} T^{2}]$ (4) $[F L^{- 3} T^{3}]$ 232. $If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:$ (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) $[h^{1/2} c^{1/2} G^{- 1/2}]$ 233. $List I A. Young’s Modulus (Y) B. Co-efficient of Viscosity (η) C. Planck’s Constant (h) D. Work Function (ϕ) List II I. [M L^{- 1} T^{- 1}] II. [M L^{2} T^{- 1}] III. [M L^{- 1} T^{- 2}] IV. [M L^{2} T^{- 2}] Choose the correct answer from the options given below:$ (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) $A-I,B-II,C-III,D-IV$ 234. $The equation of a circle is given by x^{2} + y^{2} = a^{2}, where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : (x - A t)^{2} + (y - \frac{t}{B})^{2} = a^{2} . The dimensions of t is given as [T^{- 1}] .$ (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) $A = [L^{- 1} T^{- 1}],B = [LT]$ 235. $Which of the following units denotes the dimensions M L^{2} / Q^{2}, where Q denotes the electric charge?$ (1) $H/ m^{2}$ (2) $Weber (Wb)$ (3) $Wb/ m^{2}$ (4) $Henry (H)$ 236. $The vernier constant of Vernier callipers is 0.1 mm and it has zero error of (-0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be_____x 1 0^{- 2} cm.$ 237. $The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as ..........$ 238. $Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is [Figure shows position of reference 'O' when jaws of screw gauge are closed] Given pitch =0.1cm.$ 239. $To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer find that d is proportional to S^{1/ n} . The value of n is:$ 240. $A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be where is .$