Units, Dimensions & Measurements PYQs Set 6 (PDF)

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Set 6 of 10 · Questions 151-180 of 276

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Mere Teacher · Previous Year Questions NEET Physics · Units, Dimensions & Measurements · Set 6 (Q151-180)
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151. $If force (F), velocity (V) and time (T) are taken as fundamental units, the dimensions of mass are$ (1) $F V T^{- 1}$ (2) $F V T^{- 2}$ (3) $F V^{- 1} T^{- 1}$ (4) $F V^{- 1} T$ 152. $Which of the following combinations has the dimension of electrical resistance (ϵ_{0} is the permittivity of vacuum and μ_{0} is the permeability of vacuum)?$ (1) $\frac{μ _{0}}{ϵ _{0}}$ (2) $\frac{μ _{0}}{ϵ _{0}}$ (3) $\frac{ϵ _{0}}{μ _{0}}$ (4) $\frac{ϵ _{0}}{μ _{0}}$ 153. $A quantity f is given by f = \frac{h c ^{5}}{G} where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :$ (1) $volume$ (2) $energy$ (3) $momentum$ (4) $area$ 154. $If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be$ (1) $8%$ (2) $2%$ (3) $4%$ (4) $6%$ 155. $The dimensional formula of a physical quantity represented by \frac{e ^{2}}{4 ϵ _{0} h} is [e is the charge of electron, ϵ_{0} is the permittivity of free space, and h is the Planck's constant]$ (1) $(M^{1} L^{1} T^{- 1})$ (2) $(L^{1} T^{- 1})$ (3) $(M^{1} L^{\circ} T^{- 1})$ (4) $(M^{1} L^{1} T^{- 2})$ 156. $If B is magnetic field and μ_{0} is permeability of free space, then the dimensions of (B / μ_{0}) is$ (1) $M L^{2} T^{- 2} A^{- 1}$ (2) $MT^{- 2} A^{- 1}$ (3) $L^{- 1} A$ (4) $LT^{- 2} A^{- 1}$ 157. $The dimensional formula of permeability of free space μ_{0} is$ (1) $[ML T^{- 2} A^{- 2}]$ (2) $[M^{0} L^{1} T]$ (3) $[M^{0} L^{2} T^{- 1} A^{2}]$ (4) $none of these$ 158. $The position of a particle moving on x -axis is given by x (t) = A sin t + B cos^{2} t + C t^{2} + D, where t is time. The dimension of \frac{ABC}{D} is$ (1) $L^{2} T^{- 2}$ (2) $L^{2}$ (3) $L$ (4) $L^{3} T^{- 2}$ 159. $In a photoelectric effect experiment the threshold wavelength of light is 380 nm . If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be: Given E (in eV) = \frac{1237}{λ ( in nm )}$ (1) $1.5 eV$ (2) $3.0 eV$ (3) $4.5 eV$ (4) $15.1 eV$ 160. $The physical quantity which is measured in the unit of Wb A^{- 1} is$ (1) $Self inductance$ (2) $Mutual inductance$ (3) $Magnetic flux$ (4) $Both (a) and (b)$ 161. $Consider a modified Bernoulli equation. (P + \frac{A}{B t ^{2}}) + ρg (h + Bt) + \frac{1}{2} ρ V^{2} = constant If t has the dimension of time then the dimensions of A and B are____,____respectively.$ (1) $M L^{0} T^{- 2} and M^{0} L T^{- 2}$ (2) $M L^{0} T^{- 2} and M^{0} L T^{- 1}$ (3) $M L^{0} T^{- 1} and M^{0} L T$ (4) $M L^{0} T^{- 1} and M^{0} L T^{- 1}$ 162. $The time dependence of a physical quantity p is given by = p_{0} exp (at^{2}), where a is a constant and t is the time. The constant a$ (1) $is dimensionless$ (2) $has dimensions [T^{- 2}]$ (3) $has dimensions [T^{2}]$ (4) $has dimensions of p$ 163. $The efficiency of an engine is given by η = \frac{αβ}{sin θ} \cdot log_{e} \frac{β x}{kT}, where α and β are constants. If T is the absolute temperature, k - Boltzmann constant, θ -angular displacement and x is distance, then the incorrect statement is$ (1) $Dimensions of β are same as that of force$ (2) $Dimensions of α^{- 1} x are same as that of energy$ (3) $Dimensions of η-1sinθ are same as that of αβ$ (4) $Dimensions of α are same as that of β$ 164. $In an experiment the values of two spring constants were measured as k_{1} = (10 \pm 0.2) N / m and k_{2} = (20 \pm 0.3) N / m . If these springs are connected in parallel, then the percentage error in equivalent spring constant is:$ (1) $1.33 %$ (2) $1.67 %$ (3) $2.67 %$ (4) $2.33 %$ 165. $A physical quantity z depends on four observables a, b, c and d, as z = \frac{a ^{2} b ^{\frac{2}{3}}}{c d ^{3}} . The percentages of error in the measurement of a, b, c and 2 %, 1.5 %, 4 % and 2.5 % respectively. The percentage of error in z is$ (1) $13.5 %$ (2) $14.5 %$ (3) $16.5 %$ (4) $12.25 %$ 166. $A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e ^{2}}{4 π ϵ _{0}} is [c is velocity of light, G is the universal constant of gravitation and e is charge]$ (1) $c^{2} (G \frac{e ^{2}}{4 π ϵ _{0}})^{\frac{1}{2}}$ (2) $\frac{1}{c ^{2}} (\frac{e ^{2}}{G 4 π ϵ _{0}})^{\frac{1}{2}}$ (3) $\frac{1}{c} G \frac{e ^{2}}{4 π ϵ _{0}}$ (4) $\frac{1}{c ^{2}} (G \frac{e ^{2}}{4 π ϵ _{0}})^{\frac{1}{2}}$ 167. $The dimensions of self or mutual inductance are given as$ (1) $L^{- 2} M^{1} T^{- 2} I^{- 2}$ (2) $L^{2} M^{2} T^{- 2} I^{- 2}$ (3) $L^{2} M^{1} T^{- 2} I^{- 2}$ (4) $L^{2} M^{2} T^{- 2} I^{- 1}$ 168. $A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5 mm is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively.$ (1) $Positive, 0.1 mm$ (2) $Positive, 10 μm$ (3) $Negative, 2 μm$ (4) $Positive, 0.1 μm$ 169. $The energy of a system is given as E (t) = α^{3} e^{- βt}, where t is the time and β = 0.3 s^{- 1} . The errors in the measurement of α and t are 1.2 % and 1.6 %, respectively. At t = 5 s, maximum percentage error in the energy is :$ (1) $6 %$ (2) $8.4 %$ (3) $11.6 %$ (4) $4 %$ 170. $In a typical combustion engine the workdone by a gas molecule is given by W = α^{2} β e^{\frac{- Bx ^{2}}{kT}}, where x is thedisplacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be :$ (1) $(M^{0} L T^{0})$ (2) $(M^{2} L T^{- 2})$ (3) $(ML T^{- 2})$ (4) $(ML T^{- 1})$ 171. $Match the LIST-I with LIST-II List-I (A) Magnetic induction (B) Magnetic flux (C) Magnetic permeability (D) Self inductance List-II (I) ML T^{- 2} A^{- 2} (II) ML^{2} T^{- 2} A^{- 2} (III) ML^{0} T^{- 2} A^{- 1} (IV) ML^{2} T^{- 2} A^{- 1} Choose the correct answer from the options given below:$ (1) $A-III, B-IV, C-II, D-I$ (2) $A-III, B-IV, C-I, D-II$ (3) $A-IV, B-III, C-I, D-II$ (4) $A-I, B-III, C-IV, D-II$ 172. $If absolute error is 0.05 m for a measured length of 5 m . What is the percentage error?$ (1) $1 %$ (2) $2 %$ (3) $3 %$ (4) $4 %$ 173. $Stopping potential depends on Planks constant (h), current (I), Universal gravitational constant (G) and speed of light (C) . Choose the correct option for the dimension of stopping potential (V)$ (1) $h I^{- 1} G^{1} C^{5}$ (2) $h^{- 1} I^{1} G^{- 1} C^{6}$ (3) $h^{0} I^{1} G^{1} C^{6}$ (4) $h^{0} I^{- 1} G^{- 1} C^{5}$ 174. $The pitch and the number of divisions, on the circular scale for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 division below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of the sheet is:$ (1) $5.755 mm$ (2) $5.950 mm$ (3) $5.725 mm$ (4) $5.740 mm$ 175. $Which of the following is the unit of mobility of a electron in a conductor?$ (1) $k g^{- 1} s^{2} A^{- 1}$ (2) $kg^{- 1} s^{2} A$ (3) $kg^{- 1} ms^{2} A^{- 1}$ (4) $kg ms^{- 1} A^{- 1}$ 176. $The dimensions of \frac{B ^{2}}{2 μ _{o}},where B is magnetic field and μ_{o} is the magnetic permeability of vacuum, is$ (1) $M L^{- 1} T^{- 2}$ (2) $M L^{2} T^{- 2}$ (3) $M L^{- 1} T^{2}$ (4) $M L^{- 2} T^{- 1}$ 177. $In SI units, kg m^{2} s^{- 2} is equivalent to which of the following?$ (1) $newton$ (2) $watt$ (3) $joule$ (4) $pascal$ 178. $If F_{1}, F_{2} and F_{3} are the relative strengths of the gravitational, the weak nuclear and the electromagnetic forces respectively, then$ (1) $F_{1} > F_{2} > F_{3}$ (2) $F_{1} < F_{2} < F_{3}$ (3) $F_{1} = F_{2} = F_{3}$ (4) $F_{2} > F_{3} > F_{1}$ 179. $List - I with List II. List I (A) Coefficient of viscosity (B) Intensity of wave (C) Pressure gradient (D) Compressibility List II (I) M L^{0} T^{- 3} (II) M L^{- 2} T^{- 2} (III) M^{- 1} L T^{2} (IV) M L^{- 1} T^{- 1}$ (1) $(A)-(II), (B)-(III), (C)-(IV), (D)-(I)$ (2) $(A)-(IV), (B)-(II), (C)-(I), (D)-(III)$ (3) $(A)-(IV), (B)-(I), (C)-(II), (D)-(III)$ (4) $(A)-(I), (B)-(IV), (C)-(III), (D)-(II)$ 180. $Among the following the least unit for length is$ (1) $parsec$ (2) $nanometer$ (3) $fermi$ (4) $angstrom$