HCI 01 Measurement Solutions (Discussion Questions)

1 Solutions to 2023 Measurement Discussion Questions Physical Quantities and Units D1. (A) Unit of v = -1m s Unit of   g 122 -1ms m m s     Note the use of the word “could” in the question. We do not know whether the expression is indeed correct, but to stand a chance of being correct, it has to be of the correct unit! Note also the presentation: “Unit of … = …”, and not “v = m s-1”. D2. (D). Unit of C = unit of T = unit of 3T = 1J K Unit of α = unit of unit of C / T = = J K-1 / K = J K-2 Unit of β = 3unit of unit of C / T = J K-1 / K3 = J K-4. This is on homogeneity. Take note of the working presentation of such questions: “Unit of …” D3. (C). Homogeneous implies that the units of all the terms separated by "+", "-" or “=” are the same. D4. (D). Since we can only add or subtract quantities of the same units, b should have the same unit as v, hence the unit of b is m s-1. Rearrange the equation and make k the subject, 𝑘= ଶ௉ ௗ(௩ି௕)య Unit of k = (kg m2 s-3)(kg-1 m3) / (m3 s-3) = m2 D5. (a) ampere, mole, kelvin, candela (any two) (b) The unit of energy, the joule, can be expressed in terms of base units. (c) (i) (1) massdensity=volume Unit of density, 3kg m  (2) forcepressure=area Unit of pressure, p = 2 2 m smkg  =  1 2kg m s (shown) (ii) unit of c = 1 2 1 -123 kgm s m skgm( )     (iii) It might be the speed of the gas molecules.

2 D6. (D)  Mass of a typical watermelon is about 4 to 6 kg.  Power output of a domestic electric kettle is normally from 500 to 1000 W.  Human reaction time is about 0.2 to 0.5 s.  Weight of a typical one year old baby is about 60 to 100 N (remember to multiply by g!)  Height of the overhead bridge outside Hwa Chong Institution (College) from the road surface is about 6 to 8 m What is order of magnitude? D7. (C) A smartphone is about 150 g, which corresponds to a weight of 0.15 × 9.81 ≈ 1.5 N centi: 10-2 and deci: 10-1. Errors and Uncertainties D8. (B). Because the student did not correct for zero error, his reading is off the mark by four divisions, or 0.08 100% 3.7%2.16  . With the help of the markings on the instrument, the uncertainty of his reading must be smaller than one division. Taking one division, 0.02 100% 0.93%2.16  He is precise but not accurate. D9. (B). The mean is close to the true value (small systematic error). The spread of readings is quite large (not precise). D10. (D). ΔV = 0.01 × 4.072 + 0.010 = 0.05 (1sf). Value should be expressed to the tenths place, same as the uncertainty. An unusual way to present the uncertainty. Option C can be eliminated straightaway since its uncertainty was expressed to 2 sf.

3 D11. (D) 2yL x Percentage uncertainty,                  100% 2 100%L y x L y x = 2 3% 1% 