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Physical quantities and measurement: Class 9 Physics
Base and derived quantities, SI units and prefixes, vernier calipers and screw gauge, errors, significant figures and scientific notation.
Key points
A physical quantity is anything that can be measured, such as length, mass, time and temperature. A measurement has a number and a unit, for example 5 m.
Physical quantities are of two kinds:
- Base quantities are the quantities that other quantities are built from. Length, mass, time, electric current, temperature, amount of substance and luminous intensity are the seven base quantities.
- Derived quantities are made by combining base quantities. Area, volume, speed, force and density are derived quantities.
The seven SI base units:
- Length: metre (m)
- Mass: kilogram (kg)
- Time: second (s)
- Electric current: ampere (A)
- Temperature: kelvin (K)
- Amount of substance: mole (mol)
- Luminous intensity: candela (cd)
Prefixes make very large and very small values easier to write. Kilo means 1000 (10³), mega means 10⁶, giga means 10⁹, milli means one thousandth (10⁻³), micro means 10⁻⁶ and nano means 10⁻⁹. A number written as a value between 1 and 10 multiplied by a power of ten is in scientific notation, for example 0.00056 = 5.6 × 10⁻⁴.
Measuring instruments:
- A metre rule measures length to the nearest millimetre.
- A vernier calipers measures length, thickness and diameters with a least count of 0.1 mm (0.01 cm) in the usual school instrument.
- A screw gauge measures very small thicknesses, such as the diameter of a wire, with a least count of 0.01 mm in the usual school instrument.
- A stopwatch measures time, and a measuring cylinder measures the volume of a liquid.
The least count is the smallest value an instrument can measure. If the jaws of a vernier calipers or the screw gauge show a reading when they are closed, the instrument has a zero error. A positive zero error is subtracted from the measured reading and a negative zero error is added.
Accuracy is how close a measurement is to the true value. Precision is how close repeated measurements are to one another. A measurement can be precise without being accurate. Errors come from the instrument, the method or the observer. Taking several readings and using the mean reduces random error.
Rules for significant figures:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Zeros at the start of a number are not significant (0.0045 has two).
- Zeros at the end of a number after a decimal point are significant (2.50 has three).
Study tip: Write the formula, then the substitution with units, then the answer with units. Marks are given for each step.
Definitions and flashcards
Say the meaning first, then open the card to check.
Physical quantity
A property of an object or event that can be measured.
Base quantity
A quantity that is not defined in terms of other quantities, such as length or mass.
Derived quantity
A quantity obtained by combining base quantities, such as speed.
SI units
The international system of units based on the metre, kilogram, second, ampere, kelvin, mole and candela.
Least count
The smallest value that an instrument can measure.
Zero error
The reading an instrument shows when it should show zero.
Accuracy
How close a measurement is to the true value.
Precision
How close repeated measurements are to each other.
Significant figures
The digits in a measurement that are known with certainty plus one estimated digit.
Scientific notation
A way of writing a number as a value between 1 and 10 multiplied by a power of ten.
Formula sheet
| Name | Formula | What it means |
|---|---|---|
| Least count of vernier calipers | Smallest main scale division ÷ number of vernier scale divisions | Gives the smallest length the vernier can measure. |
| Vernier reading | Main scale reading + (vernier division coinciding × least count) | The length being measured. |
| Least count of screw gauge | Pitch ÷ number of circular scale divisions | Gives the smallest length the screw gauge can measure. |
| Screw gauge reading | Linear scale reading + (circular scale reading × least count) | The thickness being measured. |
| Correct reading | Observed reading − zero error | Removes the zero error (a negative zero error is added). |
Short questions with model answers
These are the kind of questions asked for 2, 3 and 5 marks. Try each one before opening the answer.
Define a physical quantity and give two examples. (2 marks)
A physical quantity is a property that can be measured. Length and time are physical quantities.
What is the difference between a base quantity and a derived quantity? (2 marks)
A base quantity is not defined in terms of other quantities, for example length. A derived quantity is made from base quantities, for example speed, which is length divided by time.
What is meant by the least count of an instrument? (2 marks)
The least count is the smallest value that the instrument can measure accurately.
Distinguish between accuracy and precision. (2 marks)
Accuracy tells how close a measurement is to the true value. Precision tells how close repeated measurements are to each other.
Why is it better to take several readings and find the mean? (3 marks)
Every reading has a small random error. Some readings are a little too high and some a little too low. When the mean is taken these errors partly cancel, so the result is closer to the true value.
What is zero error? How is it corrected? (3 marks)
Zero error is the reading shown by an instrument when it should read zero, for example when the jaws of a vernier calipers are closed. If the zero error is positive it is subtracted from the observed reading, and if it is negative it is added.
Describe how a screw gauge is used to measure the diameter of a wire. (5 marks)
First check for zero error by closing the studs and noting the circular scale reading. Place the wire between the studs and turn the ratchet until it clicks, so the wire is held without being squeezed. Read the linear scale on the sleeve, then read the circular scale division in line with the reference line. Multiply the circular scale reading by the least count and add it to the linear scale reading. Correct for the zero error. Repeat at different places along the wire and take the mean.
Numericals with worked steps
Convert 36 km/h into m/s.
- 1 km = 1000 m and 1 h = 3600 s.
- 36 km/h = 36 × 1000 m / 3600 s.
- = 36000 / 3600 = 10 m/s.
Answer: 10 m/s
A vernier calipers has a least count of 0.01 cm. The main scale reading is 2.4 cm and the 6th vernier division is in line with a main scale division. Find the length.
- Vernier reading = main scale reading + (division in line × least count).
- = 2.4 + (6 × 0.01) cm.
- = 2.4 + 0.06 = 2.46 cm.
Answer: 2.46 cm
A screw gauge has a pitch of 1 mm and 100 divisions on the circular scale. The linear scale reads 4 mm and the circular scale reads 37. Find the thickness.
- Least count = pitch ÷ divisions = 1 mm ÷ 100 = 0.01 mm.
- Reading = linear + (circular × least count).
- = 4 + (37 × 0.01) = 4 + 0.37 = 4.37 mm.
Answer: 4.37 mm
Write 0.00056 m in scientific notation.
- Move the decimal point to get a value between 1 and 10: 5.6.
- The decimal moved 4 places to the right, so the power of ten is −4.
Answer: 5.6 × 10⁻⁴ m
How many significant figures are in 0.0450 and in 3004?
- 0.0450: the leading zeros are not significant. The digits 4, 5 and the final 0 after the decimal point are significant, so three figures.
- 3004: the zeros between non-zero digits are significant, so four figures.
Answer: 0.0450 has 3 and 3004 has 4
Common mistakes
- Forgetting to correct for zero error, or applying the correction with the wrong sign.
- Mixing units, for example adding centimetres to millimetres without converting.
- Writing the number of significant figures by counting all zeros.
- Confusing precision with accuracy: a set of readings can agree with each other and still be wrong if the instrument has a zero error.