Chapter1: Measurement

Question 1

Base qty: mass
What’s its base unit?

Answer 1

Kilogram, kg

Question 2

Base qty: length
What’s its base unit?

Answer 2

Metre, m

Question 3

Base qty: time
What’s its base unit?

Answer 3

Second, s

Question 4

Base qty: thermodynamic temperature
What’s its base unit?

Answer 4

Kelvin, K

Question 5

Base qty: electric current
What’s its base unit?

Answer 5

Ampere, A

Question 6

Base qty: amount of substance
What’s its base unit?

Answer 6

Mole, mol

Question 7

Symbol for qty is x, what is the unit of the qty?

Answer 7

[x]

Question 8

What are qtys with no base units?

Answer 8

Dimensionless qtys

Question 9

What type of eqns are definitely wrong?

Answer 9

Eqns that are not homogenous

Question 10

Eqns that are homogeneous may or may not be correct. Explain why.

Answer 10

There is:
Presence / absence of dimensionless constant
Incorrect coefficient
Presence of extra item(s) / missing item(s)

Question 11

The symbol T represents:

Answer 11

10^12

Question 12

The symbol G represents:

Answer 12

10^9

Question 13

The symbol M represents:

Answer 13

10^6

Question 14

The symbol k represents:

Answer 14

10^3

Question 15

The symbol d represents:

Answer 15

10^-1

Question 16

The symbol c represents:

Answer 16

10^-2

Question 17

The symbol m represents:

Answer 17

10^-3

Question 18

The symbol µ represents:

Answer 18

10^-6

Question 19

The symbol n represents:

Answer 19

10^-9

Question 20

The symbol p represents:

Answer 20

10^-12

Question 21

Define systematic error.

Answer 21

A systematic error is one that causes measurements to have a constant magnitude above or below true value of the measured qty. (either always positive or always negative)

Question 22

Provide examples of systematic errors.

Answer 22

Zero error
Incorrect calibration of an instrument

Question 23

How to check for and eliminate systematic errors?

Answer 23

• check for zero error
• use another instrument to take the same measurement
• plot a best fit graph / line
  (Systematic errors can be eliminated only if cause of it is found)

Question 24

Define random error.

Answer 24

A random error is one that causes measurements to have varying magnitudes and have an equal chance of being above or below the true value of the measured qty. (random error causes the set of measurements to spread about the true value)

Question 25

Give examples of random errors.

Answer 25

- parallax error (incorrect positioning of eyes while taking a reading on a measuring scale) - random human / judgement error (misjudgment of a moving object) - random variations in experimental conditions (experimenter’s hand is not steady when holding the instrument)

Question 26

State methods to minimise random error

Answer 26

- take multiple measurements and calculate average - Use a more precise instrument - plot a best fit graph / line to average out the random error

Question 27

What are the measures of error?

Answer 27

Accuracy & Precision

Question 28

Define accuracy

Answer 28

Accuracy refers to how closely a measured value agrees with the “true” value. (Affected by systematic errors)

Question 29

How do you judge accuracy of a measurement?

Answer 29

The accuracy of a measurement can be judged by comparing the closeness between the mean value and the true value. (Closer = more accurate, vice versa. Refer to notes for more specific diagrams)

Question 30

Define precision.

Answer 30

Precision refers to how closely individual measurements agree with each other without reference to any “true” value. (Affected by presence of random errors)

Question 31

How do you judge precision of a measurement?

Answer 31

The precision of a measurement can be judged by comparing the amount of spreading. (Less spreading = More precise, vice versa. Refer to notes for more specific diagrams.)

Question 32

Explain absolute uncertainty

Answer 32

Absolute uncertainty ΔX is the magnitude of the uncertainty in the measurement of a quantity X. Absolute uncertainty of X = ΔX (always expressed in 1 s.f.)

Question 33

Explain fractional uncertainty

Answer 33

Fractional uncertainty of a qty ΔX can be expressed ass a fractional of the qty X Fractional uncertainty = ΔX/X

Question 34

Explain percentage uncertainty

Answer 34

Percentage uncertainty is the fractional uncertainty multiplied by 100% to express the fraction as a percentage. Percentage uncertainty = ΔX/X * 100%

Question 35

If Z = kX, where k is a constant, the absolute uncertainty of Z is?

Answer 35

ΔZ = k ΔX

Question 36

If Z = nX ± mY, where n and m are constants, the absolute uncertainty of Z is?

Answer 36

ΔZ = n ΔX ± m ΔY

Question 37

If Z = kX^nY^m or Z = kX^n/Y^m, where k, n, and m are constants, the fractional uncertainty of Z is?

Answer 37

ΔZ/Z = |n| ΔX/X + |m| ΔY/Y

Question 38

If Z = is x, the absolute uncertainty of Z is?

Answer 38

ΔZ1 = Zmax - Z and ΔZ2 = Z - Zmin Where Zmax = sin(X + ΔX) and Zmin = sin(X - Δ X) Then take ΔZ to be the larger of the two.

Question 39

What is a scalar qty?

Answer 39

A scalar qty is one which has magnitude only.

Question 40

What is a vector qty?

Answer 40

A vector qty is one which has both magnitude and direction.