Tag: units and measurement: error analysis

Questions Related to units and measurement: error analysis

A body of mass $m =3.513\ kg$ is moving along the x-axis with a speed of $5.00{ ms }^{ -1 }$. The magnitude of its momentum is recorded as :

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $17.56\ kg{ ms }^{ -1 }$

  2. $17.57\ kg{ ms }^{ -1 }$

  3. $17.6\ kg{ ms }^{ -1 }$

  4. $17.565\ kg{ ms }^{ -1 }$

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Correct Option: C
Explanation:

Momentum$=mv=3.513\times 5.00=17.565\approx 17.57$
$\approx 17.6 kg m/s$
(Since 5.00 contains  least no. of significant figures i.e. 3)

A student measure the thickness of an object by three different instruments and gets the result as 0.5 cm, 0.50 cm, 0.500 cm. State the one which is more accurate. 

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $0.5$ cm

  2. $0.50$ cm

  3. $0.500$ cm

  4. All the measurements are equally accurate.

Show answer
Correct Option: C
Explanation:

Since, the measurement $0.500 \ cm$ gives the reading up to 3 decimel, thus $0.500 \ cm$ is the most accurate measurement among the given three measurements.

In the number 2.4560, there are 5 significant digits. Which one is the least significant digit?

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. 2

  2. 4

  3. 0

  4. 6

Show answer
Correct Option: C
Explanation:

The least significant digit is the lowest digit in a number, located at the far right of a string.


Here 0 is the rightmost side of this number so this is least significant digit.


Option C is the correct answer

Significant figures in 0.00051 are

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. 5

  2. 3

  3. 2

  4. 4

Show answer
Correct Option: C
Explanation:
In the given number  $0.00051$, the zeros to the left of the non-zero digit are not considered as significant figures.
Thus, the given number has only 2 significant figures.

Which of the following numbers has least number of significant figures?

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $0.80760$

  2. $0.80200$

  3. $0.08076$

  4. $80.267$

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Correct Option: C
Explanation:

If there is a decimal point, the rightmost digit is the last or least significant figure. So 0.08076 is the least significant figure

The number of significant figures in 10.02 is :

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. 1

  2. 2

  3. 3

  4. 4

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Correct Option: D
Explanation:

Since, all the non zero digits and zeros between the non-zero digits are considered as significant figures. Thus the number $10.02$ has $4$ significant figures.

The number of significant figures of $0.0632 m$ is :

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $5$

  2. $4$

  3. $3$

  4. $2$

Show answer
Correct Option: C
Explanation:

Zeros to the left of the non-zero digits are considered as significant figures. All non-zero digits are also considered as significant figures. Thus the number  $0.0632$ has $3$ significant figures.

Write down the significant figures in the following
1. $5238$ N
2. $4200 $kg

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $4 , 4$

  2. $4 , 2$

  3. $4, 3$

  4. $5, 3$

Show answer
Correct Option: B
Explanation:
All non-zero digits are significant and last zeros are not considered as significant.
(a) : The given number $5238$ has four significant figures.
(b) : The given number $4200$ has two significant figures.

The significant figures of the number $6.0023$ are

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $1$

  2. $5$

  3. $4$

  4. $2$

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Correct Option: B

if $L=2.331 cm$, $B = 2.1 cm$, then L+B=

physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

  1. $4.431cm$

  2. $4.43cm$

  3. $4.5cm$

  4. $4.2cm$

Show answer
Correct Option: A
Explanation:
Step 1
$L = 2.331 cm = 2.33$ (corrected to two decimal places) and $B = 2.1 cm$
Step 2
$L + B = 2.33 + 2.1 = 4.43cm. = 4.4cm$
(by the rule of addition the sum is expressed in minimum decimal places of terms in addition).