Units, Dimensions & Measurements PYQs Set 3 (PDF)

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Set 3 of 10 · Questions 61-90 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 3 (Q61-90)
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61. $If ' C^{’} and ’ V ’ represent capacity and voltage respectively then what are the dimensions of λ where C / V = λ ?$ (1) $M^{- 2} L^{- 4} I^{3} T^{7}$ (2) $M^{- 2} L^{- 3} I^{2} T^{6}$ (3) $M^{- 1} L^{- 3} I^{- 2} T^{- 7}$ (4) $M^{- 3} L^{- 4} I^{3} T^{7}$ 62. $In terms of potential difference V, electric current Ι, permittivity ε_{0}, permeability μ_{0} and speed of light c, the dimensionally correct equations(s) is(are)$ (1) $μ_{0} I^{2} = ε_{0} V^{2}$ (2) $ε_{0} I = μ_{0} V$ (3) $I = ε_{0} c V$ (4) $μ_{0} c I = ε_{0} V$ 63. $Force is given by the expression, F = A cos (Bx) + C cos (Dt), where x is displacement and t is time. The dimension of (\frac{D}{B}) is same as that of$ (1) $velocity$ (2) $velocity gradient$ (3) $angular velocity$ (4) $angular momentum$ 64. $The velocity v of a particle at time t is given by = at + \frac{b}{t + c}, where a, b and c are constants. The dimensions of a, b and c are$ (1) $[L], [LT] and [L T^{- 2}]$ (2) $[L T^{- 2}], [L] and [T]$ (3) $[L^{2}], [T] and [L T^{- 2}]$ (4) $[L T^{- 2}], [LT] and [L]$ 65. $The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be$ (1) $12%$ (2) $14%$ (3) $7%$ (4) $9%.$ 66. $A unit vector is represented as (0.8 i + bj + 0.4 k) . Hence the value of ' b' must be$ (1) $0.4$ (2) $0.6$ (3) $0.2$ (4) $0.2$ 67. $Force F is given by the equation F = \frac{X}{Linear density} . Then dimensions of X are$ (1) $(M^{2} L^{0} T^{- 2})$ (2) $(M^{0} L^{0} T^{- 1})$ (3) $(L^{2} T^{- 2})$ (4) $(M^{0} L^{2} T^{- 2})$ 68. $A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e ^{2}}{4 π ϵ _{0}} is [c is velocity of light, G is universal constant of gravitation and e is charge] [NEET 2017]$ (1) $\frac{1}{c ^{2}} (G \frac{e ^{2}}{4 π ϵ _{0}})^{1/2}$ (2) $c^{2} (G \frac{e ^{2}}{4 π ϵ _{0}})^{1/2}$ (3) $\frac{1}{c ^{2}} (\frac{e ^{2}}{G 4 π ϵ _{0}})^{1/2}$ (4) $\frac{1}{c} (G \frac{e ^{2}}{4 π ϵ _{0}})$ 69. $There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm . With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is:$ (1) $3.35 mm$ (2) $4.65 mm$ (3) $4.55 mm$ (4) $4.60 mm$ 70. $Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?$ (1) $\frac{hG}{c ^{3/2}}$ (2) $\frac{hG}{c ^{5/2}}$ (3) $\frac{hc}{G}$ (4) $\frac{Gc}{h ^{3/2}}$ 71. $The potential difference across the ends of a conductor is (50 \pm 3) V and the current through it is (5 \pm 0.1) A . The percentage error in the measurement of resistance of the conductor is$ (1) $2$ (2) $4$ (3) $8$ (4) $6$ 72. $Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be$ (1) $[M L^{2} T^{- 2}]$ (2) $[M L^{2} T^{- 1} I^{- 1}]$ (3) $[M L^{2} T^{- 3} I^{- 2}]$ (4) $[M L^{2} T^{- 3} I^{- 1}]$ 73. $If μ_{0} and ϵ_{0} are the permeability and permittivity of free space, respectively, then the dimension of (\frac{1}{μ _{0} ϵ _{0}}) is:$ (1) $T^{2} / L$ (2) $L^{2} / T^{2}$ (3) $T^{2} / L^{2}$ (4) $L / T^{2}$ 74. $Among the following, the unit of permeability is NOT represented by$ (1) $henry/metre$ (2) $weber/ampere$ (3) $ohm-second/metre$ (4) $volt-second / metre 2$ 75. $The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 μm diameter of a wire is:$ (1) $200$ (2) $50$ (3) $500$ (4) $100$ 76. $In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P = \frac{a ^{3} b ^{2}}{cd} . % error in P is$ (1) $7%$ (2) $4%$ (3) $14%$ (4) $10%$ 77. $If force [F], acceleration [a] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy. [NEET 2021]$ (1) $[F] [a] [T]$ (2) $[F] [a] (T^{2})$ (3) $[F] [a] (T^{- 1})$ (4) $[F] (a^{- 1}) [T]$ 78. $In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5mm on a complete rotation. For a particular observation the reading on the main scale is 5mm and the 2 0^{t h} division of the circular scale coincides with reference line. Calculate the true reading.$ (1) $5.00mm$ (2) $5.25mm$ (3) $5.15mm$ (4) $5.20mm$ 79. $A certain body weighs 22.42 g and has a measured volume of 4. 7 cc . The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc . Then maximum error in the density will be$ (1) $22%$ (2) $2%$ (3) $0.2%$ (4) $0.02%.$ 80. $Let x = (\frac{a ^{2} b ^{2}}{c}) be the physical quantity. If the percentage error in the measurement of physical quantities a, b and c is 2,3 and 4 percent respectively. Then percentage error in the measurement of x is$ (1) $7 %$ (2) $14 %$ (3) $21 %$ (4) $28 %$ 81. $In a RC circuit, where R is resistance and C is capacitance which of the following has the dimension of time.$ (1) $R / C$ (2) $C / R$ (3) $RC$ (4) $RC$ 82. $If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is$ (1) $(P^{\frac{1}{2}} AT^{- 1})$ (2) $(P^{2} AT^{- 2})$ (3) $[P A^{1/2} T^{- 1}]$ (4) $[PA^{- 1} T^{- 2}]$ 83. $For an experimental expression y = \frac{32.3 \times 1125}{27.4}, where all the digits are significant. Then to report the value of y we should write$ (1) $y = 1326.19$ (2) $y = 1330$ (3) $y = 1326.186$ (4) $y = 1326.2$ 84. $A screw gauge of pitch 0.5mm is used to measure the diameter of uniform wire of length 6.8cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is : [Screw gauge has 50 divisions on the circular scale]$ (1) $6. 8 c m^{2}$ (2) $3. 4 c m^{2}$ (3) $3. 9 c m^{2}$ (4) $2. 4 c m^{2}$ 85. $Choose the incorrect statement from the following:$ (1) $Strong nuclear force is a short range force.$ (2) $Weak nuclear force is weakest among gravitational. electromagnetic, weak and strong nuclear forces.$ (3) $Electromagnetic force is a long range force.$ (4) $Gravitational force acts on all objects.$ 86. $If C and R denote capacitance and resistance, the dimensional formula of CR is$ (1) $(M^{0} L^{0} T^{1})$ (2) $(M^{0} L^{0} T^{0})$ (3) $[M^{0} L^{0} T^{- 1}]$ (4) $not expressible in terms of MLT$ 87. $The ratio of the relative strengths of strong and weak nuclear forces is$ (1) $10^{13}$ (2) $10^{26}$ (3) $10^{39}$ (4) $10^{11}$ 88. $In the equation (X + \frac{a}{Y ^{2}}) (Y - b) = RT, X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the ratio \frac{a}{b} is:$ (1) $Pressure gradient$ (2) $Energy$ (3) $Impulse$ (4) $Coefficient of viscosity$ 89. $A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading: 0 mm Circular scale reading: 52 divisions Given that, 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is [NEET 2021]$ (1) $0.52 cm$ (2) $0.026 cm$ (3) $0.26 cm$ (4) $0.052 cm$ 90. $The least count of a screw guage is 0.01 mm . If the pitch is increased by 75 % and number of divisions on the circular scale is reduced by 50 %, the new least count will be \times 10^{- 3} mm$