Tag: units and measurement: error analysis

Questions Related to units and measurement: error analysis

If we weigh a given substance five times, and get 5 kg each time, then your measurement is very __________.

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

  1. Accurate

  2. Precised

  3. Accurate and Precised

  4. Cannot be judged

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Correct Option: B
Explanation:

Accuracy is defined as the extent upto which a given measurement agrees with the standard value for that measurement whereas the degree to which several measurement provide answer very close to each other is known as precision.
Since the measured values are very close to each other, then the measurements are said to be precised.

The degree to which several measurement provide answer very close to each other is known as:

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

  1. Accuracy

  2. Precision

  3. Accuracy and Precision

  4. None of these

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Correct Option: B
Explanation:

The degree to which several measurement provide answer very close to each other is known as precision.For example : Let the true weight of given substance is 12 kg.
The values of three measurements obtained by student are 10.1, 10.2 and 10.3. Then the measurements are said to be precise.

Accuracy of potentiometer can be easily increased by :

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

  1. increasing resistance of wire

  2. decreasing resistance of wire

  3. increasing the length of wire

  4. decreasing the length of wire

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Correct Option: C
Explanation:

Accuracy of potentiometer can be easily increased by decreasing the potential gradient across the potentiometer wire and that can be done by increasing its length.

________ reflects quality of measuring instrument.

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

  1. Precision

  2. Accuracy

  3. Accuracy and Precision

  4. None of these

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Correct Option: A
Explanation:

The degree to which several measurement provide answer very close to each other is known as precision. In other words, precision reflects the quality of measuring instrument.

In the context of accuracy to measurement and significant figures in expressing results of experiment, which of the following is/are correct?
(1) Out of the measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy.
(2) If one travels 478 km by rail and 397 m. by road, the total distance traveled is 478 km.

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

  1. Only (1) is correct

  2. Only (2) is correct

  3. Both are correct

  4. None of these is correct.

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Correct Option: C
Explanation:
Since for $50.14cm$
Now, the significant number$=4$
and for$0.00025$
Significant number $=2$
Both are correct

Find the maximum possible percentage error in the measurement of force on an object(on mass m) travelling at velocity v in a circle of radius r, if m=(4.0 plus minus 0.1)kg, v=(10 plus minus 0.1)m/s and r=(8.0 plus minus 0.2)m

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

  1. ( 50 ± 1) N

  2. ( 50 ± 2.5) N

  3. ( 50 ± 1.5) N

  4. ( 50 ± 3.5) N

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Correct Option: D
Explanation:

Force$(f)=\cfrac{mv^2}{r}=\cfrac{4\times(10)^2}{8}=50\ \therefore\cfrac{\Delta F}{F}=\cfrac{\Delta m}{m}+2(\cfrac{\Delta V}{V})+(\cfrac{\Delta r}{r})\ \quad=\cfrac{0.1}{4}+2\cfrac{(0.1)}{10}+\cfrac{0.8}{8}\ \therefore \cfrac{\Delta F}{F}=0.07$

Percentage error in $F=25\%+2+2.5\%$
$\therefore$ Percentage error in $F=7\%$
Eror in $\Delta F$ in $F=F\times0.07\ \quad=0\times0.07$
$\therefore$ Error in $\Delta F$ in $F=3.5N$
$\therefore F=(50\pm3.5)N$

Least count of spring balance, if a spring balance has a range of $0-25\ kg$ and consists for every $kg$ increment in weight the needle moves by $10$ divisions?

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

  1. $100\ g/mm$

  2. $0.0001\ g/mm$

  3. $0.1\ g/cm$

  4. $1\ g/m$

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Correct Option: C

The accuracy in the measurement of the diametre of a hydrogen atom as ${ 1.06\times 10 }^{ -10 }$ m is

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

  1. $0.01$

  2. ${ 106\times 10 }^{ -10 }$

  3. $\dfrac { 1 }{ 106 } $

  4. ${ 0.01\times 10 }^{ -10 }$

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Correct Option: C

Out of the following the more precise value is .....

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

  1. $1.200 \times 10 ^ { 3 } k m$

  2. $1.20 \times 10 ^ { 3 } k m$

  3. $1.2 \times 10 ^ { 3 } k m$

  4. $1200 k m$

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Correct Option: A

Which of the following reading is most accurate

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

  1. 4 cm

  2. 0.004 mm

  3. 40.00 cm

  4. 4.0 m

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Correct Option: D