Units, Dimensions & Measurements PYQs Set 5 (PDF)

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Set 5 of 10 · Questions 121-150 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 5 (Q121-150)
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121. $Match the LIST-I with LIST-II LIST-I LIST-II A. Boltzmann constant I ML^{2} T^{- 1} B Coefficient of viscosity II MLT^{- 3} K^{- 1} C Planck's constant III ML^{2} T^{- 2} K^{- 1} D Thermal conductivity IV ML^{- 1} T^{- 1} Choose the correct answer from the options given below:$ (1) $A - III, B - IV, C - I, D- II$ (2) $A - III, B - IV, C - II, D - I$ (3) $A - III, B - II, C - I, D - IV$ (4) $A - II, B - III, C - IV, D - I$ 122. $Match List - I with List - II. List-I (A) Young’s Modulus (B) Torque (C) Coefficient of Viscosity (D) Gravitational Constant List-II (I) M L^{- 1} T^{- 1} (II) ML^{- 1} T^{- 2} (III) M^{- 1} L^{3} T^{- 2} (IV) M L^{2} T^{- 2} Choose the correct answer from the options given below :$ (1) $(A)-(I), (B)-(III), (C)-(II), (D)-(IV)$ (2) $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$ (3) $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$ (4) $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$ 123. $The quantities which have the same dimensions as those of solid angle are [NEET 2024]$ (1) $strain and angle$ (2) $stress and angle$ (3) $strain and arc$ (4) $angular speed and stress$ 124. $A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e_{1} and e_{2} respectively the percentage error in the estimation of g is$ (1) $e_{2} - e_{1}$ (2) $e_{1} + 2 e_{2}$ (3) $e_{1} + e_{2}$ (4) $e_{1} - 2 e_{2}$ 125. $If A^{2} + B^{2} represents the magnitude of resultant of two vectors (A + B) and (A - B), then the angle between two vectors is$ (1) $cos^{- 1} (- \frac{2 ( A ^{2} - B ^{2} )}{( A ^{2} + B ^{2} )})$ (2) $cos^{- 1} (- \frac{A ^{2} - B ^{2}}{A ^{2} B ^{2}})$ (3) $cos^{- 1} (- \frac{( A ^{2} + B ^{2} )}{2 ( A ^{2} - B ^{2} )})$ (4) $cos^{- 1} (- \frac{( A ^{2} - B ^{2} )}{A ^{2} + B ^{2}})$ 126. $The density of a material in CGS system of units is 4 g cm^{- 3} . In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be$ (1) $0.04$ (2) $0.4$ (3) $40$ (4) $400$ 127. $If F_{1} and F_{2} are the relative strengths of the gravitational and weak nuclear forces respectively, then \frac{F _{2}}{F _{1}} is nearly$ (1) $100$ (2) $10^{39} .$ (3) $10^{13}$ (4) $10^{26}$ 128. $The ratio of the dimensions of Planck's constant and that of moment of inertia has the dimensions of$ (1) $frequency$ (2) $velocity$ (3) $time$ (4) $angular momentum.$ 129. $The true length of a wire is 3.678 cm . When the length of this wire is measured using instrument A, the length of the wire is 3.5 cm . When the length of the wire is measured using instrument B, it is found to have length 3.38 cm . Then the$ (1) $measurement with A is more accurate and precise.$ (2) $measurement with A is more accurate while measurement with B is more precise.$ (3) $measurement with B is more accurate and precise.$ (4) $measurement with A is more precise while measurement with B is more accurate.$ 130. $The expression given below shows the variation of velocity (v) with time (t), v = At^{2} + \frac{Bt}{C + t} . The dimension of ABC is :$ (1) $(M^{0} L^{1} T^{- 3})$ (2) $(M^{0} L^{2} T^{- 2})$ (3) $(M^{0} L^{1} T^{- 2})$ (4) $(M^{0} L^{2} T^{- 3})$ 131. $The number of significant figures in the numbers 4.8000 \times 10^{4} and 48000.50 are respectively$ (1) $5 and 6$ (2) $5 and 7$ (3) $2 and 7$ (4) $2 and 6$ 132. $The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 \times 1 0^{- 3} are$ (1) $5, 1, 2$ (2) $5, 1, 5$ (3) $5, 5, 2$ (4) $4, 4, 2$ 133. $If E and G respectively denote energy and gravitational constant, then E / G has the dimensions of [NEET 2021]$ (1) $M^{2} L^{- 1} T^{0}$ (2) $[M] L^{- 1} T^{- 1}$ (3) $[M] L^{0} T^{0}$ (4) $M^{2} L^{- 2} T^{- 1}$ 134. $Which pair do not have equal dimensions?$ (1) $Energy and torque$ (2) $Force and impulse$ (3) $Angular momentum and Planck constant$ (4) $Elastic modulus and pressure.$ 135. $Match the LIST-I with LIST-II List-I (A) Spring constant (B) Thermal conductivity (C) Boltzmann constant (D) Inductive reactance List-II (I) ML^{2} T^{- 2} K^{- 1} (II) ML^{0} T^{- 2} (III) ML^{2} T^{- 3} A^{- 2} (IV) MLT^{- 3} K^{- 1} Choose the correct answer from the options given below:$ (1) $A-II, B-IV, C-I, D-III$ (2) $A-I, B-IV, C-II, D-III$ (3) $A-II, B-I, C-IV, D-III$ (4) $A-III, B-II, C-IV, D-I$ 136. $The diameter and height of a cylinder are measured by a meter scale to be 12.6 \pm 0.1 cm and 34.2 \pm 0.1 cm respectively. What will be the value of its volume in appropriate significant figures?$ (1) $4264 \pm 81 cm^{3}$ (2) $4264.4 \pm 81.0 cm^{3}$ (3) $4260 \pm 80 cm^{3}$ (4) $4300 \pm 80 cm^{3}$ 137. $Let G, W, E and S be relative strength of gravitational, weak-nuclear, electromagnetic and strong-nuclear forces, respectively. Which of the correct statement?$ (1) $S > W > E > G$ (2) $E > W > S > G$ (3) $S > E > W > G$ (4) $S > E > G > W$ 138. $Given below are two statements: Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. choose the correct answer from the options given below.$ (1) $Statement I is true but Statement II is false$ (2) $Statement I is false but Statement II is true$ (3) $Both Statement I and Statement II are false$ (4) $Both Statement I and Statement II are true$ 139. $For the four sets of three measured physical quantities as given below. Which of the following options is correct? (i) A_{1} = 24.36, B_{1} = 0.0724, C_{1} = 256.2 (ii) A_{2} = 24.44, B_{2} = 16.082, C_{2} = 240.2 (iii) A_{3} = 25.2, B_{3} = 19.2812, C_{3} = 236.183 (iv) A_{4} = 25, B_{1} = 236.191, C_{4} = 19.5$ (1) $A_{1} + B_{1} + C_{1} < A_{3} + B_{3} + C_{3} < A_{2} + B_{2} + C_{2} < A_{4} + B_{4} + C_{4}$ (2) $A_{1} + B_{1} + C_{1} = A_{2} + B_{2} + C_{2} = A_{3} + B_{3} + C_{3} = A_{4} + B_{4} + C_{4}$ (3) $A_{4} + B_{4} + C_{4} < A_{1} + B_{1} + C_{1} = A_{2} + B_{2} + C_{2} = A_{3} + B_{3} + C_{3}$ (4) $A_{4} + B_{4} + C_{4} < A_{2} + B_{2} + C_{2} < A_{1} + B_{1} + C_{1} = A_{3} + B_{3} + C_{3}$ 140. $A physical quantity S is related to four observables a, b, c, d as S = \frac{a b}{c ^{3} d ^{4}} . If the percentage errors of measurement in a, b, c, d are 2 %, 1 %, 1 % and 1 % respectively, then percentage error in the quantity S is$ (1) $6 %$ (2) $8 %$ (3) $9 %$ (4) $10 %$ 141. $If N_{A}, N_{B} and. N_{C} are the number of significant figures in A = 0.001204 m, B = 43120000 m and c = 1.200 m respectively then$ (1) $N_{A} = N_{B} = N_{C}$ (2) $N_{A} > N_{B} > N_{C}$ (3) $N_{A} < N_{B} < N_{C}$ (4) $N_{A} > N_{B} < N_{C}$ 142. $Two protons are kept at a separation of 10 nm . Let F_{n} and F_{e} be the nuclear force and the electromagnetic force between them$ (1) $F_{e} ≪ F_{n}$ (2) $F_{e} = F_{n}$ (3) $F_{e} and F_{n} differ only slightly$ (4) $F_{e} >> F_{n}$ 143. $Time intervals measured by a clock give the following readings 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s. What is the percentage relative error of the observations? [NEET 2020]$ (1) $2%$ (2) $4%$ (3) $16%$ (4) $1.6%$ 144. $A screw gauge gives the following reading when used to measure the diameter of a wire . Main scale reading : 0 mm Circular scale reading : 52 division Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is :$ (1) $0.52 cm$ (2) $0.052 cm$ (3) $0.026 cm$ (4) $0.005 cm$ 145. $In the formula X = 5 Y Z^{2}, X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?$ (1) $[M^{- 3} L^{- 2} T^{8} A^{4}]$ (2) $[M^{- 1} L^{- 2} T^{4} A^{2}]$ (3) $[M^{- 2} L^{0} T^{- 4} A^{- 2}]$ (4) $[M^{- 2} L^{- 2} T^{6} A^{3}]$ 146. $A quantity x is given by (IF v^{2} / W L^{4}) in terms of moment of inertia I, force F, velocity v, work W and length L . The dimensional formula for x is same as that of$ (1) $Coefficient of viscosity$ (2) $Force constant$ (3) $Energy density$ (4) $Planck's constant$ 147. $For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm):$ (1) $0.002$ (2) $0.0025$ (3) $0.0005$ (4) $0.001$ 148. $If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:$ (1) $E V^{- 1} T^{- 2}$ (2) $E V^{- 2} T^{- 2}$ (3) $E^{- 2} V^{- 1} T^{- 3}$ (4) $E V^{- 2} T^{- 1}$ 149. $The dimensions of 'resistance' are same as those of. where h is the Planck's constant, e is the charge.$ (1) $\frac{h ^{2}}{e ^{2}}$ (2) $\frac{h ^{2}}{e}$ (3) $\frac{h}{e ^{2}}$ (4) $\frac{h}{e}$ 150. $A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t, given by t = A ρ^{a} r^{b} η^{c} σ^{d}, where A is a constant and a, b, c and d are integers. The value of \frac{b + c}{a + d} is____.$