Tag: accuracy, precision and uncertainty in measurement

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Questions Related to accuracy, precision and uncertainty in measurement

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

The mean length of an object is $5\ cm$. Which of the following measurements is most accurate?

  1. $4.9\ cm$

  2. $4.805\ cm$

  3. $5.25\ m$

  4. $5.4\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the problem, the length L = 5 cm 

Let us first check the error in each value by picking options one by one, we get
$\triangle L _1 = 5 -4.9 = 0.1 cm$
$\triangle L _2  = 5 -4.805 = 0.195 cm$
$\triangle L _3 = 5.25 - 5 = 0.25 cm$
$\triangle L _4 = 5.4 -5 = 0.4 cm$
Hence Error $\triangle L _1$ is least.
Hence 4.9 cm is most closer to true value. So 4.9 is more accurate.

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

When the jaws of a vernier callipers are in contact with each other, the zeroeth division of the vernier scale does not coincide with the zeroeth division. of the main scale but coincides with the second division on it. Discuss the accuracy of the observed readings done with the instrument

  1. Accuracy decreases.

  2. Accuracy increases

  3. no change

  4. cant say
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A zero error occurs when the instrument does not read zero when it should. This introduces a systematic error, which decreases the accuracy of the readings unless corrected.

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

Why are shields made of iron usually provided around precision instruments?

  1. For protection against the effect of moisture in the air

  2. For guiding the instruments against unauthorised handling

  3. For protection against the effect of external magnetic fields

  4. For absorbing heat generated during the functioning of the instruments
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 Metals like iron can be used to shield the instruments from external magnetic fields because magnetic fields cannot penetrate metallic surfaces.

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

The length of two rods measured by a meter scale are 60.0 cm and 20.0 cm respectively. The least count of meter scale is 1 mm. Then

  1. First measurement is more accurate

  2. Second measurement is more accurate

  3. Both measurement are equally accurate

  4. First measurement is more is more precise
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

The time of 25 oscillations of a simple pendulum is measured to be $50.0 s$ by a watch of least count $0.1 s$. The percentage error in time is

  1. $0.2 \%$

  2. $0.02 \%$

  3. $0.002 \%$

  4. $2 \%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total time is 50.0 s with a least count of 0.1 s. The absolute error is 0.1 s. Percentage error = (absolute error / total time) * 100 = (0.1 / 50.0) * 100 = 0.2%.

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

The error in the measurement of length of a simple pendulum is $0.1\%$ and error in the time period is $2 \%$. The possible maximum error in the quantity having dimensional formula $LT^{-2}$ is

  1. $1.1 \%$

  2. $2.2\%$

  3. $4.1\%$

  4. $6.1\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given,

Error $\%$ in time $=2\%=\dfrac{2}{100}=\dfrac{1}{50}=2\%$
Error $\%$ in length $=1\%$
Find $\%$ error in $\dfrac{1}{12}$
$\therefore$ as $\dfrac{\triangle A}{A}=\left( \dfrac{\triangle 2}{2}\right) +\left( \dfrac{\triangle Q}{Q}\right)$    if $A=\dfrac{t}{Q}$
Thus, 
$\Rightarrow \%$ error $=\left( \dfrac{\triangle L}{L}\right) +2\left( \dfrac{\triangle T}{T}\right)$
                   $=\left( 2\%\right) +2\left( .1\%\right)$
                   $=2\%+.2\%$
                   $=2.2\%$
Hence, the answer is $2.2\%.$

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

Which of the following measurements is most accurate?

  1. $0.005 mm$

  2. $5.00 mm$

  3. $50.00 mm$

  4. $5.0 mm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Accuracy in measurement is often indicated by the number of significant figures and the relative error. 50.00 mm has the most significant figures and the smallest relative error among the choices.

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

The mathematical operation in which the accuracy is limited to least accurate term is :

  1. addition

  2. subtraction

  3. multiplication and division

  4. both A and B
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In addition or subtraction we can reduce the terms to least accurate term and add or subtract them. By this process in addition or subtraction answer is not much get affected or change in answer is negligible.

But if we apply this process in multiplication and division, change in answer is considerable.
Hence in addition and subtraction accuracy is limited to least accurate term.