Measurements and Experimentation
ICSE Class 9 · Physics · Chapter 1
What this chapter covers
- Physical quantities and systems of units
- Least count and accuracy
- Vernier callipers
- Micrometre screw gauge
- Simple pendulum
- Simple numerical problems on instrument readings
Key points
- A physical quantity is expressed as a numerical value multiplied by a unit.
- Length, mass and time are fundamental quantities in mechanics; area, speed and density are derived quantities.
- The three systems of units are fps (foot, pound, second), cgs (centimetre, gram, second) and SI (metre, kilogram, second, with seven fundamental units in all).
- Unit symbols take no plural and no full stop; a symbol named after a person starts with a capital letter.
- 1 g cm-3 = 1000 kg m-3.
- The least count is the smallest value an instrument can measure correctly; a smaller least count gives greater accuracy.
- Vernier callipers: LC = 1 M.S.D. − 1 V.S.D. = 0.1 mm for the usual instrument; reading = M.S.R. + coincidence × LC.
- Screw gauge: LC = pitch ÷ number of circular divisions = 0.01 mm for pitch 1 mm and 100 divisions.
- Zero error is positive when the instrument reads more than zero with nothing in it; corrected reading = observed reading − zero error (with sign).
- The effective length of a pendulum runs from the point of suspension to the centre of the bob.
- T = 2π√(l/g) for small amplitudes; T does not depend on the mass of the bob or on a small amplitude.
- f = 1/T; the time period is found by timing 20 oscillations and dividing by 20.
- The graph of l against T2 is a straight line through the origin, and g = 4π2 × slope.
Questions answered
Define a unit, and give the SI units of mass and time.
A unit is a fixed, agreed amount of a physical quantity used as the standard for measuring it. The SI unit of mass is the kilogram (kg) and of time the second (s).
Distinguish between a fundamental unit and a derived unit, with one example of each.
A fundamental unit is defined independently of other units (metre); a derived unit is formed from fundamental units by multiplication or division (m s-1 for speed).
Name the units of length, mass and time in the cgs and fps systems.
cgs: centimetre, gram, second. fps: foot, pound, second.
Point out the mistakes in "a bag of 5 Kgs. of rice" and rewrite it correctly.
The symbol kg takes a small k, no plural s and no full stop: "a bag of 5 kg of rice".
Why does a smaller least count give a more accurate measurement?
The least count is the smallest step the instrument can show, so the possible error in a reading is at most about one least count; a smaller step means a smaller possible error.
A Vernier scale has 10 divisions that equal 9 mm of the main scale. What is its least count?
1 V.S.D. = 0.9 mm, so LC = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm.
With the jaws of a Vernier callipers closed, the Vernier zero is to the left of the main scale zero and the 6th division coincides. The LC is 0.01 cm. What is the zero error, and what is the correction?
Zero error = −(10 − 6) × 0.01 cm = −0.04 cm. The correction is +0.04 cm.
Define the pitch of a screw gauge. A screw gauge of pitch 0.5 mm has 50 circular divisions. What is its least count?
The pitch is the distance moved by the spindle for one complete rotation of the thimble. LC = 0.5 mm ÷ 50 = 0.01 mm.
Past board exam questions
ICSE 2019 sample paper · 2 marks
(i) Define the least count of an instrument. (ii) What is the least count of a standard laboratory micrometer screw gauge?
Show answer
(i) The least count of an instrument is the smallest measurement that can be made accurately with it.
(ii) The least count of a standard laboratory micrometer screw gauge is 0.001 cm (= 0.01 mm).
ICSE 2019 sample paper · 2 marks
Two pendulums P and Q have equal lengths but their bobs weigh 10gf and 20gf respectively. (i) Compare their time periods. (ii) Give a reason for your answer.
Show answer
(i) Their time periods are equal (ratio 1 : 1).
(ii) The time period of a simple pendulum, T = 2π√((l)/(g)), depends only on its effective length and g; it does not depend on the mass (weight) of the bob. Since the lengths are equal, the time periods are equal.