Units, instruments and the care needed to measure length, mass, time and volume.
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To measure is to compare with a standard. A physical quantity has a magnitude and a unit. Fundamental quantities (length, mass, time, temperature, electric current, luminous intensity) have their own units in the SI system: metre, kilogram, second, kelvin, ampere, candela. Derived quantities are built from them: area (m²), volume (m³), density (kg/m³), speed (m/s). Convert carefully: 1 km = 1000 m, 1 h = 3600 s, 1 m³ = 10⁶ cm³ = 1000 L.
Convert 72 km/h into m/s.
72 × 1000 ÷ 3600 = 20 m/s.
A block is 5 cm × 4 cm × 2 cm and has mass 160 g. Find its volume and density.
Volume = 5 × 4 × 2 = 40 cm³. Density = 160 ÷ 40 = 4 g/cm³.
Convert 2.5 m³ to litres.
2.5 × 1000 = 2500 L.
The least count is the smallest value an instrument can read. For a vernier caliper, least count = 1 MSD − 1 VSD; if 10 vernier divisions equal 9 main-scale divisions of 1 mm, it is 0.1 mm = 0.01 cm. Reading = main scale reading + (vernier coincidence × least count). A screw gauge has least count = pitch ÷ number of circular scale divisions, e.g. 1 mm ÷ 100 = 0.01 mm, and is used for thin wires. Correct for any zero error before using the reading.
A vernier has main scale reading 4.2 cm and the 3rd vernier division coincides (least count 0.01 cm). Find the reading.
4.2 + 3 × 0.01 = 4.23 cm.
Find the least count of a screw gauge of pitch 1 mm with 100 divisions.
1 mm ÷ 100 = 0.01 mm.
What is zero error and how is it corrected?
The reading shown when the jaws are closed; subtract a positive zero error and add a negative one.
A measurement is never exact. Take several readings and find their mean to reduce random error. Avoid parallax by keeping the eye directly above the mark. Use the instrument with the suitable least count: a metre rule for a table, vernier for a coin, a screw gauge for a wire. Quote the answer with the correct unit and a sensible number of digits.
Why take the mean of several readings?
It reduces the effect of random errors in individual readings.
What is parallax?
The apparent shift of a reading when the eye is not placed straight above the mark.
Which instrument measures the diameter of a thin wire?
A screw gauge.
1. Name the SI unit of mass and of time.
2. Give two derived quantities with units.
3. Convert 108 km/h into m/s.
4. Define least count.
5. Mass 160 g and volume 40 cm³: find the density in kg/m³.
6. What is a fundamental quantity?
7. How does a vernier caliper read 0.01 cm?
8. Why is the mean of readings taken?
9. Convert 5000 cm³ into litres.
10. State one source of error in measuring with a metre rule.