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SI units and prefixes questions
Almost every quantity in physics carries a unit, and every unit is built from the same six blocks. Learn the blocks, the ten prefixes that scale them, and the ratios that come out with no unit at all. Then carry the units through the calculation itself, because bolting them on at the end is where the last mark goes missing.
19 original questions · 53 marks · the si units and prefixes notes · Measurements
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Name the six SI base quantities used at A-level and the SI base unit of each.
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Mass (kilogram, kg) and length (metre, m) (1); time (second, s) and electric current (ampere, A) (1); temperature (kelvin, K) and amount of substance (mole, mol) (1). One mark for each two correct pairs.Convert (a) 5.0 km into metres and (b) 2.5 GHz into hertz.
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(a) 5.0 km = 5000 m, that is 5.0 × 103 m (1)
(b) 2.5 GHz = 2.5 × 109 Hz (1)Express the newton (N) in terms of SI base units.
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From F = ma (1), 1 N = 1 kg m s−2 (1).A capacitor is labelled 85 pF and a nuclear radius is quoted as 2.4 fm. Write (a) 85 pF in farads and (b) 2.4 fm in metres, each in standard form.
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(a) 85 pF = 8.5 × 10−11 F (1). (b) 2.4 fm = 2.4 × 10−15 m (1).A photon of red light has an energy of 3.2 × 10−19 J. 1 eV = 1.60 × 10−19 J. Calculate the photon energy in electronvolts.
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Energy in eV = energy in J ÷ (1.60 × 10−19) (1) = 3.2 × 10−19/(1.60 × 10−19) = 2.0 eV (1).Express (a) the joule and (b) the watt in SI base units.
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(a) J = N m (1) = kg m2 s−2 (1). (b) W = J s−1 = kg m2 s−3 (1).Convert (a) 3.0 mA into amperes, (b) 450 nm into metres and (c) 12 MΩ into ohms.
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(a) 3.0 mA = 3.0 × 10−3 A (1). (b) 450 nm = 4.5 × 10−7 m (1). (c) 12 MΩ = 1.2 × 107 Ω (1).Use base units to check whether the equation v2 = 2as is homogeneous (dimensionally consistent).
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LHS: (m s−1)2 = m2 s−2 (1)
RHS: a × s = (m s−2)(m) = m2 s−2 (1)
Both sides have the same units, so the equation is homogeneous (1)Express the pascal (Pa) in SI base units.
A domestic oven transfers energy at a rate of 2.4 kW. It runs for 90 minutes. Calculate the energy transferred (a) in kilowatt hours and (b) in joules. (1 kW h = 3.6 × 106 J.)
The cross-sectional area of a copper track on a circuit board is 0.020 mm2. Express this area in m2, in standard form.
Four lasers emit light of wavelength 580 nm, 0.65 μm, 6.2 × 10−7 m and 0.00071 mm. By converting each wavelength to metres in standard form, place the four in order of increasing wavelength.
The period of a simple pendulum is given by T = 2π√(l/g), where l is a length and g is the gravitational field strength in m s−2. Show that the unit of √(l/g) is the second.
The gravitational constant G appears in F = GMm/r2. Determine the SI base units of G.
Convert (a) a density of 2.7 g cm−3 into kg m−3 and (b) a speed of 90 km h−1 into m s−1.
Explain why checking that an equation is homogeneous (has matching units on both sides) is a useful way to spot mistakes.
A pulsed laser delivers pulses of energy 2.5 mJ, each lasting 6.0 ns. Calculate the average power of one pulse in watts, and express your answer using an appropriate SI prefix.
A student cannot remember whether the speed of a wave on a stretched string is v = √(T/μ) or v = √(μ/T), where T is the tension in newtons and μ is the mass per unit length in kg m−1. Deduce, using base units, which of the two equations could be correct.
An electricity supplier charges 28p per kilowatt hour. A 3.0 kW immersion heater runs for 2.0 hours each day. Determine the cost of running the heater for a 30-day month.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
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