A metal wire has mass \((0.4\pm 0.002)~\mathrm{g}\), radius \((0.3\pm 0.001)~\mathrm{mm}\) and length \((5\pm 0.02)~\mathrm{cm}\). The maximum possible percentage error in the measurement of density will nearly be:
1. \(1.4 \%\)
2. \(1.2 \%\)
3. \(1.3 \%\)
4. \(1.6 \%\)
Subtopic:  Errors |
From NCERT
NEET - 2023
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The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
1. Random errors
2. Instrumental errors
3. Personal errors
4. Least count errors
Subtopic:  Errors |
 67%
From NCERT
NEET - 2023
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The determination of the value of acceleration due to gravity \((g)\) by simple pendulum method employs the formula,
 \(g=4\pi^2\frac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
1.  \(\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)\)
2.  \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]\)
3.  \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]\)
4.  \(\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)\)

Subtopic:  Errors |
 76%
From NCERT
NEET - 2022
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The percentage error in the measurement of \(g\) is:
[Given,  \(g=\frac{4\pi^2L}{T^2},L=(10\pm0.1)~\text{cm, }T=(100\pm1)~\text s\)]
1. \(2\%\)
2. \(5\%\)
3. \(3\%\)
4. \(7\%\)
Subtopic:  Errors |
 73%
From NCERT
NEET - 2022
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Time intervals measured by a clock give the following readings: 
\(1.25\) s, \(1.24\) s, \(1.27\) s, \(1.21\) s and \(1.28\) s. 
What is the percentage relative error of the observations? 
1. \(2\)%
2. \(4\)%
3. \(16\)%
4. \(1.6\)%

Subtopic:  Errors |
From NCERT
NEET - 2020
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In an experiment, the percentage errors that occurred in the measurement of physical quantities \(A,\) \(B,\) \(C,\) and \(D\) are \(1\%\), \(2\%\), \(3\%\), and \(4\%\) respectively. Then, the maximum percentage of error in the measurement of \(X,\) where \(X=\frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3}\), will be:
1. \(10\%\)
2. \(\frac{3}{13}\%\)
3. \(16\%\)
4. \(-10\%\)

Subtopic:  Errors |
 85%
From NCERT
NEET - 2019
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In an experiment, four quantities \(a,\) \(b,\) \(c\) and \(d\) are measured with percentage error \(1\)%, \(2\)%, \(3\)% and \(4\)% respectively. Quantity \(P\) is calculated as follows: 
\(P=\frac{a^3b^2}{cd}\)
Percentage error in \(P\) is:
1. \(10\%\)
2. \(7\%\)
3. \(4\%\)
4. \(14\%\)
Subtopic:  Errors |
 89%
From NCERT
AIPMT - 2013
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A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate \(g,\) the acceleration due to gravity. If the maximum percentage errors in the measurement of the distance and the time are \(e_1\) and \(e_2\) respectively, the percentage error in the estimation of \(g\) is:
1. e1+2e2
2. e1+e2
3. e1-2e2
4. e2-e1

Subtopic:  Errors |
 66%
From NCERT
AIPMT - 2010
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If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:

1. 4%

2. 6%

3. 8%

4. 2%

Subtopic:  Errors |
 83%
From NCERT
AIPMT - 2008
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If the error in measurement of the radius of a sphere is 0.1%, then the error in its volume will be:
1. 0.3%
2. 0.4%
3. 0.5%
4. 0.6%

Subtopic:  Errors |
 89%
From NCERT
AIPMT - 1999
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