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Q. No.
A physical quantity \(Q \) depends on other physical quantities \(a, b\) and \(c\) as \(Q=\dfrac{a^4 b^3}{c^2}.\) If the maximum percentage error in measurement of \(a. b\) and \(c\) are \(3\%, 4\%\) and \(5\%\) respectively, then the maximum percentage error in measurement of \(Q\) is:
1. \(34\%\)
2. \(40\%\)
3. \(32\%\)
4. \(45\%\)
Subtopic:  Errors |
 88%
Level 1: 80%+
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Pressure on a circular plate is obtained by measuring the force and the radius of the plate. If the error in measuring force and radius is \(1\%\) and \(0.5\%\) respectively, then the error in pressure is:
1. \(1\%\)
2. \(2\%\)
3. \(6\%\)
4. \(8\%\)
Subtopic:  Errors |
 87%
Level 1: 80%+
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If the error in the measurement of mass is \(0.8\%\) and in volume it is \(0.4 \%,\) then the error in the measurement of density is:
1. \(1.2 \%\)
2. \(0.4 \%\)
3. \(0.8\%\)
4. \(1 \%\)
Subtopic:  Errors |
 88%
Level 1: 80%+
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Two resistances, \(R_1=(60\pm6)~\Omega\) and \(R_2=(40\pm2)~\Omega\) are connected in series. The equivalent resistance will be:
1. \(100\pm12~\Omega\)
2. \(100\pm10~\Omega\)
3. \(100\pm8~\Omega\)
4. \(100\pm4~\Omega\)
Subtopic:  Errors |
 87%
Level 1: 80%+
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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 |
 85%
Level 1: 80%+
AIPMT - 1999
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A physical quantity, \(y=\dfrac{a^{4} b^{2}}{\left(c d^{4}\right)^{1 / 3}}\) has four observables \(a,\) \(b,\) \(c\) and \(d.\) The percentage error in \(a,\) \(b,\) \(c\) and \(d\) are \(2\text{%},\) \(3\text{%},\) \(4\text{%}\) and \(5\text{%}\) respectively. The error in \(y\) is:
1. \(6\text{%}\) 2. \(11\text{%}\)
3. \(12\text{%}\) 4. \(22\text{%}\)
Subtopic:  Errors |
 85%
Level 1: 80%+
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The angular momentum of a rotating sphere of mass-\(m,\) radius-\(r\) is computed from the expression: \(L=\dfrac25mr^2\omega,\) where \(\omega\) is the angular speed of rotation. The mass is known to within \(0.5\%,\) the radius to \(0.5\%,\) and the angular speed \((\omega)\) to within \(1\%.\) The fractional error in \(L\) is:
1. \(1\%\) 2. \(1.5\%\)
3. \(2\%\) 4. \(2.5\%\)
Subtopic:  Errors |
 85%
Level 1: 80%+
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The error in the measurement of distance is \(2\%,\) while that in time is \(1\%.\) The error in speed, computed from the above, is:
1. \(2\%+1\%\) 2. \(2\%-1\%\)
3. \(\dfrac{2\%+1\%}{2}\) 4. \(\dfrac{2\%-1\%}{2}\)
Subtopic:  Errors |
 84%
Level 1: 80%+
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The relative error in \(Z,\) if \(Z=\dfrac{A^{4}B^{1/3}}{CD^{3/2}}\) is:

1. \(\dfrac{\Delta A}{A}+\dfrac{\Delta B}{B}+\dfrac{\Delta C}{C}+\dfrac{\Delta D}{D}\)

2. \(4\dfrac{\Delta A}{A}+\dfrac{1}{3}\dfrac{\Delta B}{B}-\dfrac{\Delta C}{C}- \dfrac{3}{2}\dfrac{\Delta D}{D}\)

3. \(4\dfrac{\Delta A}{A}+\dfrac{1}{3}\dfrac{\Delta B}{B}+\dfrac{\Delta C}{C}+\dfrac{2}{3}\dfrac{\Delta D}{D}\)

4. \(4\dfrac{\Delta A}{A}+\dfrac{1}{3}\dfrac{\Delta B}{B}+\dfrac{\Delta C}{C}+\dfrac{3}{2}\dfrac{\Delta D}{D}\)

Subtopic:  Errors |
 82%
Level 1: 80%+
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Which of the following measurement is most precise?
1. \(5.00~\text{mm}\) 
2. \(5.00~\text{cm}\) 
3. \(5.00~\text{m}\) 
4. \(5.00~\text{km}\) 

Subtopic:  Errors |
 81%
Level 1: 80%+
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