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Accuracy, precision and uncertainty in measurement - class-IX

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Are senses reliable for accurate measurement?

  1. True

  2. False


Correct Option: B
Explanation:

Our senses are not reliable for accurate measurement.

Which of the following time measuring devices is most precise?

  1. A wall clock

  2. An atomic clock

  3. A digital watch

  4. stop watch


Correct Option: B
Explanation:

Option $(B)$ is correct because a clock can measure time correctly up to one second. A stopwatch can measure time correctly up to a fraction of a second. A digital watch can measure time up to a fraction of second whereas an atomic clock is the most accurate timekeeper and is based on characteristic frequencies of radiation emitted by certain atoms having a precision of about $1$ second in $300,000$ years. So an atomic clock can measure time most precisely as the precision of this clock is about $1 s$ in $10^{13} s$.

 Students A, B and C measure the diameter of a wire using three different screw gauges of least count  0.01 cm, 0.05 cm and 0.001 cm respectively. Each one makes 10 measurements.The measurements will be more precise for 

  1. A

  2. B

  3. C

  4. all


Correct Option: C
Explanation:

For a screw gauge, the precision in measurement is depends on the least count. The smaller least count will give the more precision. Since student C has measured diameter using screw gauge with smallest least count so the measurement will more precise for student C.   

Students A,B and C measure the diameter of a copper ball using the same screw gauge. A takes 5 readings, B takes 9 readings and C takes 8 readings. The measured value will be most accurate for

  1. B

  2. A

  3. C

  4. all


Correct Option: A
Explanation:

The accuracy is how close the measured value with the true value. The true value is the average value of the measurements. Thus when more number measurements will be taken, the accuracy will be more. Since student B has taken more readings, so the measured value for B will be most accurate.   

In lab one student obtained a weight measurement of $3.2 kg$ for a given substance, but the actual or known weight is $10 kg$, then his measurement is :

  1. accurate

  2. not accurate

  3. precised

  4. not presiced


Correct Option: B
Explanation:

Since the measured value of weight of the substance is far away from the value of actual weight, so the measurement is said to be inaccurate.

 If measurements for a given substance are close to the known value, but the measurements are far from each other, then you have _______ without _______. Fill the appropriate answers.

  1. Accuracy, Precision

  2. Precision, Accuracy

  3. This situation is not possible

  4. None of these


Correct Option: A
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 measurements are close to the known value. so these measurements are accurate but these are far from each other, these are not precised.

The mass of an object is measured by two students (true weight is 12 kg)
Student 1: He measures 12 kg
Student 2: She measures 12.5 kg
Measurement of which student is more accurate.

  1. Student 1

  2. Student 2

  3. Both are equally accurate

  4. Cannot be compared.


Correct Option: A
Explanation:

Accuracy defines nearness of a measured value to the standard or true value. Since value measured by student 1 is nearer to the actual value $12 \ kg$ compared to that measured by student 2. So measurement of student 1 is more accurate.

The extent to which a given measurement agrees with the standard value for that measurement is known as :

  1. Accuracy

  2. Precision

  3. Accuracy and Precision

  4. None of these


Correct Option: A
Explanation:

Accuracy is defined as the extent upto which a given measurement agrees with the standard value for that measurement.
For example : Actual weight of the given substance is $10.0 \ kg$ and the measured value of the mass is $9.9 \ kg$. This measurement is said to be accurate.

________ refers to the degree of conformity and correctness of something when compared to a true or absolute value. Fill the appropriate answer.

  1. Accuracy

  2. Precision

  3. Accuracy and Precision

  4. None of these


Correct Option: A
Explanation:

Accuracy is defined as the extent upto which a given measurement agrees with the standard value for that measurement. Accuracy refers to the degree of conformity and correctness of something when compared to a true or absolute value.

_______ refers to a state of strict exactness.Fill the appropriate answer.

  1. Accuracy

  2. Precision

  3. Accuracy and Precision

  4. None of these.


Correct Option: B
Explanation:

Precision refers to a state of strict exactness.
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.

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

  1. Accurate

  2. Precised

  3. Accurate and Precised

  4. Cannot be judged


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:

  1. Accuracy

  2. Precision

  3. Accuracy and Precision

  4. None of these


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 :

  1. increasing resistance of wire

  2. decreasing resistance of wire

  3. increasing the length of wire

  4. decreasing the length of wire


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.

  1. Precision

  2. Accuracy

  3. Accuracy and Precision

  4. None of these


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.

  1. Only (1) is correct

  2. Only (2) is correct

  3. Both are correct

  4. None of these is correct.


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

  1. ( 50 ± 1) N

  2. ( 50 ± 2.5) N

  3. ( 50 ± 1.5) N

  4. ( 50 ± 3.5) N


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?

  1. $100\ g/mm$

  2. $0.0001\ g/mm$

  3. $0.1\ g/cm$

  4. $1\ g/m$


Correct Option: C

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

  1. $0.01$

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

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

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


Correct Option: C

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

  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. $1200 k m$


Correct Option: A

Which of the following reading is most accurate

  1. 4 cm

  2. 0.004 mm

  3. 40.00 cm

  4. 4.0 m


Correct Option: D

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. $5.4\ cm$


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

  1. Accuracy decreases.

  2. Accuracy increases

  3. no change

  4. cant say


Correct Option: A

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


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

  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


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

  1. $0.2 \%$

  2. $0.02 \%$

  3. $0.002 \%$

  4. $2 \%$


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

  1. $1.1 \%$

  2. $2.2\%$

  3. $4.1\%$

  4. $6.1\%$


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?

  1. $0.005 mm$

  2. $5.00 mm$

  3. $50.00 mm$

  4. $5.0 mm$


Correct Option: C

Which is most accurate?

  1. 3 m

  2. 3.0 m

  3. 3.00 m

  4. 3.000 m


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 :

  1. addition

  2. subtraction

  3. multiplication and division

  4. both A and B


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.

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