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 possible range of error in measurement

B) The average value only

C) The unit of measurement

D) The exact value of the quantity

2 / 35

If two quantities are added, their absolute uncertainties are:

A) Added

B) Multiplied

C) Divided

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

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

4 / 35

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

A) $\mathbf{5.1\ cm}$

B) $\mathbf{0.02\ cm}$

C) $\mathbf{0.1\ cm}$

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) $\mathbf{1.0\ cm}$

B) $\mathbf{0.6\ cm}$

C) $\mathbf{0.1\ cm}$

D) $\mathbf{0.3\ cm}$

6 / 35

Fractional uncertainty is calculated as:

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

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

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

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

7 / 35

Percentage uncertainty is:

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

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

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

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

8 / 35

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

A) $\mathbf{0.25}$

B) $\mathbf{2.5}$

C) $\mathbf{0.04}$

D) $\mathbf{4}$

9 / 35

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

A) $\mathbf{2\%}$

B) $\mathbf{4\%}$

C) $\mathbf{25\%}$

D) $\mathbf{50\%}$

10 / 35

When multiplying quantities, the fractional uncertainties are:

A) Multiplied

B) Subtracted

C) Added

D) Ignored

11 / 35

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

A) Adding fractional uncertainties

B) Subtracting percentage uncertainties

C) Adding absolute uncertainties

D) Dividing absolute uncertainties

12 / 35

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

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

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

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) Three times the percentage uncertainty in length

B) Same as length uncertainty

C) Nine times length uncertainty

D) Half of length uncertainty

14 / 35

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

A) Remains constant

B) Decreases

C) Becomes zero always

D) Increases

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

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

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

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

16 / 35

For a derived quantity involving subtraction, the uncertainties are:

A) Multiplied

B) Subtracted

C) Added

D) Divided

17 / 35

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

A) $\mathbf{5\%}$

B) $\mathbf{10\%}$

C) $\mathbf{0.5\%}$

D) $\mathbf{50\%}$

18 / 35

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

A) Multiplying absolute uncertainties

B) Ignoring time uncertainty

C) Subtracting uncertainties

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

19 / 35

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

A) $\mathbf{12\%}$

B) $\mathbf{6\%}$

C) $\mathbf{5\%}$

D) $\mathbf{1\%}$

20 / 35

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

A) $\mathbf{8\%}$

B) $\mathbf{4\%}$

C) $\mathbf{2\%}$

D) $\mathbf{6\%}$

21 / 35

Which type of uncertainty is used when adding measured lengths?

A) Relative uncertainty only

B) Percentage uncertainty

C) Absolute uncertainty

D) Fractional uncertainty

22 / 35

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

A) $\mathbf{0.05\%}$

B) $\mathbf{20\%}$

C) $\mathbf{5\%}$

D) $\mathbf{50\%}$

23 / 35

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

A) $\mathbf{7\%}$

B) $\mathbf{12\%}$

C) $\mathbf{1\%}$

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

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

25 / 35

If a measurement has smaller percentage uncertainty, it is:

A) Less reliable

B) Impossible to compare

C) More reliable

D) Always inaccurate

26 / 35

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

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

B) Largest uncertainty only

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

D) Average uncertainty

27 / 35

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

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

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

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 allow comparison between different measurements.

B) They change units.

C) They give exact values.

D) They remove all errors.

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) Worst-case error estimate

B) Minimum error

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) $\mathbf{0.02}$

B) $\mathbf{0.3}$

C) $\mathbf{15}$

D) $\mathbf{0.1}$

32 / 35

The uncertainty in a calculated quantity depends on:

A) Units only

B) Uncertainties of measured quantities

C) Formula length only

D) Only its numerical value

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) Ignoring volume uncertainty

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

D) Subtracting uncertainties

34 / 35

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

A) Halves

B) Doubles

C) Remains unchanged

D) Becomes zero

35 / 35

Which statement is correct about uncertainty?

A) It is always equal to zero.

B) Better instruments reduce uncertainty.

C) It has no effect on derived quantities.

D) It can never be reduced.

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