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Physics: All Topics
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What is the SI unit of length, and what are its symbol and usual laboratory sub-units?
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Cambridge IGCSE Physics
Physics: All TopicsComplete deck
01·1.1 Physical quantities and measurement techniques
What is the SI unit of length, and what are its symbol and usual laboratory sub-units?
Answer
The metre (m). Lengths are also commonly given in kilometres (km), centimetres (cm) and millimetres (mm).
02·1.1 Physical quantities and measurement techniques
State the conversions between km, m, cm and mm.
Answer
1 km = 1000 m; 1 m = 100 cm = 1000 mm; 1 cm = 10 mm.
03·1.1 Physical quantities and measurement techniques
What do the multipliers M, k, c and m stand for, and what is each worth?
Answer
M = mega = × 10⁶; k = kilo = × 10³; c = centi = × 10⁻²; m = milli = × 10⁻³.
04·1.1 Physical quantities and measurement techniques
What do the multipliers G, µ and n stand for, and what is each worth?
Answer
G = giga = × 10⁹; µ = micro = × 10⁻⁶; n = nano = × 10⁻⁹. (Extended candidates must be able to use these.)
05·1.1 Physical quantities and measurement techniques
Which measuring instrument would you choose to measure (a) the length of a pencil, (b) the length of a laboratory bench?
Answer
(a) A 30 cm ruler graduated in mm. (b) A metre rule (or tape measure) graduated in mm. Choose an instrument whose range covers the length in one measurement and whose smallest division gives suitable precision.
06·1.1 Physical quantities and measurement techniques
What is the smallest division on a standard laboratory ruler, and to what precision should a length be recorded with it?
Answer
1 mm. Record lengths to the nearest mm (e.g. 7.6 cm or 76 mm); where the end falls between marks you may interpolate to the nearest half division (0.5 mm).
07·1.1 Physical quantities and measurement techniques
What is parallax error?
Answer
An error in reading a scale caused by the eye not being directly in line with (perpendicular to) the scale mark, so the reading appears shifted. It is avoided by looking straight at the scale at 90° to it.
08·1.1 Physical quantities and measurement techniques
What is the SI unit of volume, and which units are normally used in the laboratory?
Answer
SI unit: cubic metre (m³). In the laboratory cm³ (= ml) and dm³ (= litre) are used: 1 dm³ = 1000 cm³.
09·1.1 Physical quantities and measurement techniques
How many cm³ are there in 1 m³?
Answer
1 m³ = 100 cm × 100 cm × 100 cm = 1 000 000 cm³ = 10⁶ cm³ (so 1 cm³ = 10⁻⁶ m³).
10·1.1 Physical quantities and measurement techniques
Which instrument is used to measure the volume of a liquid directly?
Answer
A measuring cylinder (graduated in cm³ or ml).
11·1.1 Physical quantities and measurement techniques
What is a meniscus, and which part of it do you read for water?
Answer
The curved surface of a liquid in a narrow container. For water (and most liquids) it curves downwards, so the reading is taken at the bottom of the meniscus.
12·1.1 Physical quantities and measurement techniques
State the equation for the volume of a rectangular block.
Answer
Volume = length × breadth (width) × height, V = l × b × h. Units: e.g. cm × cm × cm = cm³.
13·1.1 Physical quantities and measurement techniques
State the equation for the volume of a cylinder.
Answer
V = πr²h, where r is the radius of the circular cross-section and h is the height (length) of the cylinder.
14·1.1 Physical quantities and measurement techniques
State the equations for the area of a rectangle, a triangle and a circle.
Answer
Rectangle: A = length × breadth. Triangle: A = ½ × base × height. Circle: A = πr².
15·1.1 Physical quantities and measurement techniques
Describe how to measure the length of a small object, such as a pencil, accurately with a ruler.
Answer
Place the ruler flat and close alongside the object, parallel to it. Line one end of the object up with the zero mark (or note the starting reading). Look perpendicular to the scale at the other end to avoid parallax, read to the nearest mm, and subtract the start reading if not zero.
16·1.1 Physical quantities and measurement techniques
Why should you avoid measuring from the very end of a ruler?
Answer
The end may be worn or damaged, and many rulers have a gap before the zero mark. Measuring from the end introduces a systematic (zero) error; instead align with the zero mark or take two readings and subtract.
17·1.1 Physical quantities and measurement techniques
Describe how to use a measuring cylinder to find the volume of a liquid correctly.
Answer
Stand the cylinder on a flat, horizontal surface so it is vertical. Wait for the liquid to settle. Put your eye level with the bottom of the meniscus (avoids parallax) and read the scale, interpolating to the nearest half division if needed. Record with the unit cm³.
18·1.1 Physical quantities and measurement techniques
Why should a measuring cylinder be placed on a horizontal surface before it is read?
Answer
So the cylinder is vertical and the liquid surface is level with the scale markings; a tilted cylinder gives an incorrect reading.
19·1.1 Physical quantities and measurement techniques
Describe how to find the volume of an irregularly shaped solid (e.g. a stone) using a measuring cylinder.
Answer
Partly fill a measuring cylinder with water and read the volume V₁. Lower the solid in gently on a thread so it is fully submerged and no water splashes out. Read the new volume V₂. Volume of solid = V₂ − V₁ (displacement method).
20·1.1 Physical quantities and measurement techniques
A measuring cylinder has 2 cm³ divisions. The bottom of the meniscus lies exactly halfway between the 36 cm³ and 38 cm³ marks. What is the reading?
Answer
37 cm³ — interpolate to the nearest half of the smallest division.
21·1.1 Physical quantities and measurement techniques
Why is a 50 cm³ measuring cylinder better than a 250 cm³ cylinder for measuring about 40 cm³ of water?
Answer
The smaller cylinder has finer (smaller) scale divisions, so the volume can be read more precisely and the percentage uncertainty is smaller. Choose the smallest cylinder that holds the whole volume.
22·1.1 Physical quantities and measurement techniques
Describe how to measure the diameter of a ball or cylinder using a ruler and two set squares (or wooden blocks).
Answer
Place the object on the bench against a ruler. Put a set square (or block) against each side so they touch the object and are perpendicular to the ruler. The diameter is the distance between the two set-square edges, read from the ruler (difference between the two readings).
23·1.1 Physical quantities and measurement techniques
How can you make sure a ruler used to measure a height above a bench is vertical, and why does it matter?
Answer
Check it against a set square standing on the bench (or use a stand and clamp). If the ruler is tilted, the reading is larger than the true vertical height — a systematic error.
24·1.1 Physical quantities and measurement techniques
What is a zero error, and how is it corrected?
Answer
A zero error exists when an instrument does not read zero when it should (or its zero mark is not at the start of the scale). Correct by adding or subtracting the zero error from every reading, as appropriate.
25·1.1 Physical quantities and measurement techniques
Calculate the volume of a wooden block 40 cm long, 12 cm wide and 5.0 cm high, in cm³ and in m³.
Answer
V = 40 × 12 × 5.0 = 2400 cm³. Since 1 cm³ = 10⁻⁶ m³, V = 2400 × 10⁻⁶ = 2.4 × 10⁻³ m³.
26·1.1 Physical quantities and measurement techniques
Calculate the volume of a cylinder of radius 10 mm and height 5.0 cm, giving the answer in m³.
Answer
r = 10 mm = 1.0 cm. V = πr²h = π × (1.0 cm)² × 5.0 cm = 15.7 ≈ 16 cm³ = 16 × 10⁻⁶ m³ = 1.6 × 10⁻⁵ m³.
27·1.1 Physical quantities and measurement techniques
Convert an area of 25 cm² into m².
Answer
1 cm² = (10⁻² m)² = 10⁻⁴ m², so 25 cm² = 25 × 10⁻⁴ m² = 2.5 × 10⁻³ m².
28·1.1 Physical quantities and measurement techniques
A rectangular block measures 4.1 cm × 2.8 cm × 2.1 cm. Calculate its volume to an appropriate number of significant figures.
Answer
V = 4.1 × 2.8 × 2.1 = 24.108 cm³. The data are given to 2 significant figures, so V = 24 cm³ (2 s.f.).
29·1.1 Physical quantities and measurement techniques
How many significant figures are there in (a) 7.180 cm and (b) 0.042 cm?
Answer
(a) 4 s.f. — the final zero is significant because it shows the precision of the measurement. (b) 2 s.f. — leading zeros are not significant.
30·1.1 Physical quantities and measurement techniques
A student records the length of an object measured with a mm ruler as '7 cm'. Why is this poor practice, and how should it be recorded?
Answer
Readings should reflect the precision of the instrument. A mm ruler can measure to 0.1 cm, so it should be recorded as 7.0 cm (or 70 mm).