Physics 11th Chap 1 : Topic 5 - Maryam Publications

Physics Chapter 1 : Topic 5

Uncertainty in Derived Quantities

1 / 35

The uncertainty in a measured quantity represents:

A) The average value only

B) The exact value of the quantity

C) The possible range of error in measurement

D) The unit of measurement

2 / 35

If two quantities are added, their absolute uncertainties are:

A) Multiplied

B) Divided

C) Added

D) Ignored

3 / 35

If $\mathbf{A = B + C\ }$, the uncertainty in $\mathbf{A}$ is:

A) $\mathbf{\Delta A = \Delta B + \Delta C}$

B) $\mathbf{\Delta A = \Delta B - \Delta C}$

C) $\mathbf{\Delta A = \Delta B\ /\ \Delta C}$

D) $\mathbf{\Delta A = \Delta B \times \Delta C}$

4 / 35

A length is measured as $\mathbf{5.0 \pm 0.1\ cm}$. The uncertainty is:

A) $\mathbf{5.1\ cm}$

B) $\mathbf{0.1\ cm}$

C) $\mathbf{0.02\ cm}$

D) $\mathbf{5.0\ cm}$

5 / 35

If length $\mathbf{l}\mathbf{= 20 \pm 0.2\ cm}$ and width $\mathbf{w = 10 \pm 0.1\ cm}$, uncertainty in perimeter $\mathbf{P = 2(}\mathbf{l}\mathbf{+ w)}$ is:

A) $\mathbf{0.3\ cm}$

B) $\mathbf{0.6\ cm}$

C) $\mathbf{0.1\ cm}$

D) $\mathbf{1.0\ cm}$

6 / 35

Fractional uncertainty is calculated as:

A) Uncertainty $\mathbf{+}$ measured value

B) Measured value $\mathbf{/}$ uncertainty

C) Uncertainty $\mathbf{\times}$ measured value

D) Uncertainty $\mathbf{/}$ measured value

7 / 35

Percentage uncertainty is:

A) Fractional uncertainty $\mathbf{\times 100}$

B) Value $\mathbf{\times 100}$

C) Absolute uncertainty $\mathbf{\times}$ value

D) Fractional uncertainty $\mathbf{\div 100}$

8 / 35

A mass is measured as $\mathbf{\pm \ 2\ g}$. Its fractional uncertainty is:

A) $\mathbf{4}$

B) $\mathbf{0.25}$

C) $\mathbf{0.04}$

D) $\mathbf{2.5}$

9 / 35

The percentage uncertainty in $\mathbf{50 \pm 2\ g}$ is:

A) $\mathbf{25\%}$

B) $\mathbf{4\%}$

C) $\mathbf{50\%}$

D) $\mathbf{2\%}$

10 / 35

When multiplying quantities, the fractional uncertainties are:

A) Subtracted

B) Added

C) Ignored

D) Multiplied

11 / 35

If $\mathbf{(Q = AB)}$, the uncertainty in $\mathbf{Q}$ is found by:

A) Dividing absolute uncertainties

B) Adding absolute uncertainties

C) Subtracting percentage uncertainties

D) Adding fractional uncertainties

12 / 35

If $\mathbf{Q =}$ $\frac{\mathbf{A}}{\mathbf{B}}\mathbf{\ }$, then fractional uncertainty in $\mathbf{Q}$ is:

A) $\frac{\mathbf{\Delta A}}{\mathbf{A}}\mathbf{+}\frac{\mathbf{\Delta B}}{\mathbf{B}}$

B) $\mathbf{\Delta A - \Delta B}$

C) $\mathbf{\Delta A + \Delta B}$

D) $\frac{\mathbf{\Delta A}}{\mathbf{A}}\mathbf{-}\frac{\mathbf{\Delta B}}{\mathbf{B}}$

13 / 35

The volume of a cube is $\mathbf{V =}\mathbf{l}^{\mathbf{3}}$. The percentage uncertainty in volume is approximately:

A) Nine times length uncertainty

B) Half of length uncertainty

C) Three times the percentage uncertainty in length

D) Same as length uncertainty

14 / 35

If the uncertainty in length measurement is reduced, the uncertainty in volume:

A) Remains constant

B) Decreases

C) Increases

D) Becomes zero always

15 / 35

A rectangle has length $\mathbf{20 \pm 1\ cm}$ and width $\mathbf{\pm \ 0.5\ cm}$. The maximum absolute uncertainty in area is:

A) $\mathbf{15}\mathbf{\ cm}^{\mathbf{2}}$

B) $\mathbf{30}\mathbf{\ cm}^{\mathbf{2}}$

C) $\mathbf{200\ }\mathbf{cm}^{\mathbf{2}}$

D) $\mathbf{1.5}\mathbf{\ cm}^{\mathbf{2}}$

16 / 35

For a derived quantity involving subtraction, the uncertainties are:

A) Divided

B) Added

C) Multiplied

D) Subtracted

17 / 35

If $\mathbf{l}\mathbf{= 10 \pm 0.5\ m}$, percentage uncertainty is:

A) $\mathbf{0.5\%}$

B) $\mathbf{50\%}$

C) $\mathbf{5\%}$

D) $\mathbf{10\%}$

18 / 35

A velocity is calculated using $\mathbf{v =}$ $\frac{\mathbf{s}}{\mathbf{t}}$. The percentage uncertainty in velocity is found by:

A) Adding percentage uncertainties of $\mathbf{s}$ and $\mathbf{t}$

B) Multiplying absolute uncertainties

C) Ignoring time uncertainty

D) Subtracting uncertainties

19 / 35

If distance has $\mathbf{2\%}$ uncertainty and time has $\mathbf{3\%}$ uncertainty, uncertainty in velocity is:

A) $\mathbf{5\%}$

B) $\mathbf{12\%}$

C) $\mathbf{1\%}$

D) $\mathbf{6\%}$

20 / 35

If radius of a sphere has $\mathbf{2\%}$ uncertainty, uncertainty in its volume is:

A) $\mathbf{2\%}$

B) $\mathbf{4\%}$

C) $\mathbf{6\%}$

D) $\mathbf{8\%}$

21 / 35

Which type of uncertainty is used when adding measured lengths?

A) Absolute uncertainty

B) Fractional uncertainty

C) Relative uncertainty only

D) Percentage uncertainty

22 / 35

A measured quantity is$\mathbf{\ }\mathbf{100 \pm 5}$ units. Its percentage uncertainty is:

A) $\mathbf{5\%}$

B) $\mathbf{50\%}$

C) $\mathbf{0.05\%}$

D) $\mathbf{20\%}$

23 / 35

If two quantities have percentage uncertainties of $\mathbf{4\%}$ and $\mathbf{3\%}$, the percentage uncertainty in their product is:

A) $\mathbf{1\%}$

B) $\mathbf{7\%}$

C) $\mathbf{12\%}$

D) $\mathbf{0.75\%}$

24 / 35

A derived quantity $\mathbf{Q =}\mathbf{A}^{\mathbf{2\ }}\mathbf{B}$. The fractional uncertainty in $\mathbf{Q}$ is:

A) $\frac{\mathbf{\Delta A}}{\mathbf{A}}\mathbf{+}\frac{\mathbf{\Delta B}}{\mathbf{B}}$

B) $\frac{\mathbf{\Delta A}}{\mathbf{A}}\mathbf{\ .\ \ }\frac{\mathbf{\Delta B}}{\mathbf{B}}$

C) $\mathbf{2}$ $\frac{\mathbf{\Delta A}}{\mathbf{A}}\mathbf{+}\frac{\mathbf{\Delta B}}{\mathbf{B}}$

D) $\mathbf{2}$ $\frac{\mathbf{\Delta B}}{\mathbf{B}}\mathbf{+}\frac{\mathbf{\Delta A}}{\mathbf{A}}$

25 / 35

If a measurement has smaller percentage uncertainty, it is:

A) Impossible to compare

B) Less reliable

C) More reliable

D) Always inaccurate

26 / 35

The uncertainty in $\mathbf{A + B + C}$ is:

A) Largest uncertainty only

B) Average uncertainty

C) $\mathbf{\Delta A + \Delta B + \Delta C}$

D) $\mathbf{\Delta A\ \Delta B\ \Delta C}$

27 / 35

A quantity is calculated as $\mathbf{Q}\mathbf{=}$ $\frac{\mathbf{a}^{\mathbf{2}}}{\mathbf{b}}$. The fractional uncertainty is:

A) $\mathbf{2}$ $\frac{\mathbf{\Delta a}}{\mathbf{a}}\mathbf{-}\frac{\mathbf{\Delta b}}{\mathbf{b}}$

B) $\frac{\mathbf{\Delta a}}{\mathbf{a}}\mathbf{+}\frac{\mathbf{\Delta b}}{\mathbf{b}}$

C) $\mathbf{2}$ $\frac{\mathbf{\Delta a}}{\mathbf{a}}\mathbf{+}\frac{\mathbf{\Delta b}}{\mathbf{b}}$

D) $\frac{\mathbf{\Delta a}}{\mathbf{a}}\mathbf{\times}\frac{\mathbf{\Delta b}}{\mathbf{b}}$

28 / 35

Why are percentage uncertainties useful?

A) They remove all errors.

B) They change units.

C) They give exact values.

D) They allow comparison between different measurements.

29 / 35

A measurement with uncertainty $\mathbf{\pm \ 0.01\ cm}$ is generally:

A) Less precise than $\mathbf{\pm \ 1\ cm}$

B) Impossible to compare

C) Equally precise

D) More precise than $\mathbf{\pm \ 1\ cm}$

30 / 35

The maximum possible uncertainty method gives:

A) Minimum error

B) Worst-case error estimate

C) Average error

D) Exact value

31 / 35

If $\mathbf{A = 5 \pm 0.1\ }$and $\mathbf{B = 10 \pm 0.2}$, uncertainty in $\mathbf{A + B}$ is:

A) $\mathbf{0.1}$

B) $\mathbf{0.02}$

C) $\mathbf{0.3}$

D) $\mathbf{15}$

32 / 35

The uncertainty in a calculated quantity depends on:

A) Only its numerical value

B) Units only

C) Formula length only

D) Uncertainties of measured quantities

33 / 35

A student calculates density $\mathbf{\rho = m\ V}$. The uncertainty calculation requires:

A) Adding fractional uncertainties of $\mathbf{m}$ and $\mathbf{V}$

B) Subtracting uncertainties

C) Adding absolute uncertainties of $\mathbf{m}$ and $\mathbf{V}$

D) Ignoring volume uncertainty

34 / 35

If the uncertainty in a quantity doubles while the value remains constant, its percentage uncertainty:

A) Remains unchanged

B) Becomes zero

C) Halves

D) Doubles

35 / 35

Which statement is correct about uncertainty?

A) It has no effect on derived quantities.

B) It can never be reduced.

C) Better instruments reduce uncertainty.

D) It is always equal to zero.

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