Units, Dimensions & Measurements PYQs Set 6 (PDF)

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Set 6 of 10 · Questions 151-180 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 6 (Q151-180)
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151. $The dimensional formula of angular momentum is$ (1) $[M L^{2} T^{- 2}]$ (2) $[M L^{- 2} T^{- 1}]$ (3) $[ML T^{- 1}]$ (4) $[M L^{2} T^{- 1}]$ 152. $Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is:$ (1) $0.08$ (2) $0.06$ (3) $0.18$ (4) $0.24$ 153. $Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as$ (1) $2.124 cm$ (2) $2.123 cm$ (3) $2.125 cm$ (4) $2.121 cm$ 154. $Dimensional formula for the universal gravitational constant G is$ (1) $M^{- 1} L^{3} T^{- 2}$ (2) $M^{- 1} L^{3} T^{- 1}$ (3) $M^{- 1} L^{2} T^{- 2}$ (4) $M^{0} L^{0} T^{0}$ 155. $Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is$ (1) $ML^{2} T^{- 2}$ (2) $MLT^{- 2}$ (3) $M^{2} L^{0} T^{- 1}$ (4) $ML^{0} T^{- 3}$ 156. $If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is:$ (1) $0.0002 cm$ (2) $0.001 cm$ (3) $0.01 cm$ (4) $0.02 cm$ 157. $If force (F), velocity (V) and time (T) are taken as fundamental units, the dimensions of mass are$ (1) $F V T^{- 1}$ (2) $F V T^{- 2}$ (3) $F V^{- 1} T^{- 1}$ (4) $F V^{- 1} T$ 158. $Which of the following combinations has the dimension of electrical resistance (ϵ_{0} is the permittivity of vacuum and μ_{0} is the permeability of vacuum)?$ (1) $\frac{μ _{0}}{ϵ _{0}}$ (2) $\frac{μ _{0}}{ϵ _{0}}$ (3) $\frac{ϵ _{0}}{μ _{0}}$ (4) $\frac{ϵ _{0}}{μ _{0}}$ 159. $A quantity f is given by f = \frac{h c ^{5}}{G} where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :$ (1) $volume$ (2) $energy$ (3) $momentum$ (4) $area$ 160. $If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be$ (1) $8%$ (2) $2%$ (3) $4%$ (4) $6%$ 161. $Identify the incorrect statement among the following.$ (1) $A true length of 5.678 km has been measured in two experiments as 5.5 km and 5.51 km, respectively. The second measurement has more precision.$ (2) $Length of 1m and 0.5 m have been both measured with the same absolute error of 0.01 m . Both the measurement are equally accurate.$ (3) $The numbers of significant digits in 1.6 and 0.60 are both two.$ (4) $The number 2.445 can be rounded to two decimal . place as 2.45 .$ 162. $The dimensional formula of a physical quantity represented by \frac{e ^{2}}{4 ϵ _{0} h} is [e is the charge of electron, ϵ_{0} is the permittivity of free space, and h is the Planck's constant]$ (1) $(M^{1} L^{1} T^{- 1})$ (2) $(L^{1} T^{- 1})$ (3) $(M^{1} L^{\circ} T^{- 1})$ (4) $(M^{1} L^{1} T^{- 2})$ 163. $If B is magnetic field and μ_{0} is permeability of free space, then the dimensions of (B / μ_{0}) is$ (1) $M L^{2} T^{- 2} A^{- 1}$ (2) $MT^{- 2} A^{- 1}$ (3) $L^{- 1} A$ (4) $LT^{- 2} A^{- 1}$ 164. $The dimensional formula of permeability of free space μ_{0} is$ (1) $[ML T^{- 2} A^{- 2}]$ (2) $[M^{0} L^{1} T]$ (3) $[M^{0} L^{2} T^{- 1} A^{2}]$ (4) $none of these$ 165. $The position of a particle moving on x -axis is given by x (t) = A sin t + B cos^{2} t + C t^{2} + D, where t is time. The dimension of \frac{ABC}{D} is$ (1) $L^{2} T^{- 2}$ (2) $L^{2}$ (3) $L$ (4) $L^{3} T^{- 2}$ 166. $In a photoelectric effect experiment the threshold wavelength of light is 380 nm . If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be: Given E (in eV) = \frac{1237}{λ ( in nm )}$ (1) $1.5 eV$ (2) $3.0 eV$ (3) $4.5 eV$ (4) $15.1 eV$ 167. $The physical quantity which is measured in the unit of Wb A^{- 1} is$ (1) $Self inductance$ (2) $Mutual inductance$ (3) $Magnetic flux$ (4) $Both (a) and (b)$ 168. $Consider a modified Bernoulli equation. (P + \frac{A}{B t ^{2}}) + ρg (h + Bt) + \frac{1}{2} ρ V^{2} = constant If t has the dimension of time then the dimensions of A and B are____,____respectively.$ (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) $M L^{0} T^{- 1} and M^{0} L T^{- 1}$ 169. $The time dependence of a physical quantity p is given by = p_{0} exp (at^{2}), where a is a constant and t is the time. The constant a$ (1) $is dimensionless$ (2) $has dimensions [T^{- 2}]$ (3) $has dimensions [T^{2}]$ (4) $has dimensions of p$ 170. $The efficiency of an engine is given by η = \frac{αβ}{sin θ} \cdot log_{e} \frac{β x}{kT}, where α and β are constants. If T is the absolute temperature, k - Boltzmann constant, θ -angular displacement and x is distance, then the incorrect statement is$ (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) $Dimensions of α are same as that of β$ 171. $In an experiment the values of two spring constants were measured as k_{1} = (10 \pm 0.2) N / m and k_{2} = (20 \pm 0.3) N / m . If these springs are connected in parallel, then the percentage error in equivalent spring constant is:$ (1) $1.33 %$ (2) $1.67 %$ (3) $2.67 %$ (4) $2.33 %$ 172. $A physical quantity z depends on four observables a, b, c and d, as z = \frac{a ^{2} b ^{\frac{2}{3}}}{c d ^{3}} . The percentages of error in the measurement of a, b, c and 2 %, 1.5 %, 4 % and 2.5 % respectively. The percentage of error in z is$ (1) $13.5 %$ (2) $14.5 %$ (3) $16.5 %$ (4) $12.25 %$ 173. $A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e ^{2}}{4 π ϵ _{0}} is [c is velocity of light, G is the universal constant of gravitation and e is charge]$ (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) $\frac{1}{c ^{2}} (G \frac{e ^{2}}{4 π ϵ _{0}})^{\frac{1}{2}}$ 174. $The dimensions of self or mutual inductance are given as$ (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) $L^{2} M^{2} T^{- 2} I^{- 1}$ 175. $A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5 mm is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively.$ (1) $Positive, 0.1 mm$ (2) $Positive, 10 μm$ (3) $Negative, 2 μm$ (4) $Positive, 0.1 μm$ 176. $The energy of a system is given as E (t) = α^{3} e^{- βt}, where t is the time and β = 0.3 s^{- 1} . The errors in the measurement of α and t are 1.2 % and 1.6 %, respectively. At t = 5 s, maximum percentage error in the energy is :$ (1) $6 %$ (2) $8.4 %$ (3) $11.6 %$ (4) $4 %$ 177. $In a typical combustion engine the workdone by a gas molecule is given by W = α^{2} β e^{\frac{- Bx ^{2}}{kT}}, where x is thedisplacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be :$ (1) $(M^{0} L T^{0})$ (2) $(M^{2} L T^{- 2})$ (3) $(ML T^{- 2})$ (4) $(ML T^{- 1})$ 178. $In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of (M^{a} L^{b} T^{c}) . If b = - 3, the value of c is .$ 179. $A physical quantity C is related to four other quantities p, q, r and s as follows C = \frac{p q ^{2}}{r ^{3} s} The percentage errors in the measurement of p, q, r and s are 1 %, 2 %, 3 % and 2 %, respectively. The percentage error in the measurement of C will be ________%$ 180. $The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is (\frac{x}{100}) % If the relative errors in measuring the mass and the diameter are 6.0 % and 1.5 % respectively, the value of x is$