Tag: units and measurement: error analysis

Questions Related to units and measurement: error analysis

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

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

  1. $4.9\ cm$

  2. $4.805\ cm$

  3. $5.25\ m$

  4. $5.4\ cm$

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Correct Option: A
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.

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

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

  1. Accuracy decreases.

  2. Accuracy increases

  3. no change

  4. cant say

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Correct Option: A

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

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

  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

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Correct Option: C
Explanation:

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

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

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

  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

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Correct Option: C,D

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

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

  1. $0.2 \%$

  2. $0.02 \%$

  3. $0.002 \%$

  4. $2 \%$

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Correct Option: A

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

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

  1. $1.1 \%$

  2. $2.2\%$

  3. $4.1\%$

  4. $6.1\%$

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Correct Option: B
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 $2.2\%.$

Which of the following measurements is most accurate?

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

  1. $0.005 mm$

  2. $5.00 mm$

  3. $50.00 mm$

  4. $5.0 mm$

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Correct Option: C

Which is most accurate?

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

  1. 3 m

  2. 3.0 m

  3. 3.00 m

  4. 3.000 m

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Correct Option: D
Explanation:

The one with more significant figures in the decimal is more accurate.
Option D.

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

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

  1. addition

  2. subtraction

  3. multiplication and division

  4. both A and B

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Correct Option: D
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.

The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is:

physics units and measurement: error analysis rounding off digits rounding of digits standard form

  1. 2.3 kg

  2. 2.34 kg

  3. 2.340 kg

  4. 2.3403 kg

Show answer
Correct Option: A
Explanation:

Here, mass of the box, $m = 2.3 kg$
Mass of one gold piece, $m _1 = 20.15 g = 0.02015 kg$
Mass of other gold piece, $m _2 = 20.17 g = 0.02017 kg$
$\therefore$ Total mass = $m + m _1 +m _2 = 2.3 kg + 0.02015 kg +0.02017 kg = 2.34032 kg$
As the result is correct only upto one place of decimal, therefore, on rounding off, we get Total mass $= 2.3 kg$