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Units and Measurements
Propagation of Errors
2 questions from 2 papers, each with its answer.
- questions
- 2
- papers
- 2
- years asked, 2017–2026
- 1 of 10
- of Units and Measurements
- 3.77%
Appears in
Concepts tested
- Combination of Percentage Errors
- Percentage error in a power relation
All Questions
2025 1 question
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A physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows: $P = a^3 b^2 / c\sqrt{d}$. The percentage errors of measurement in $a, b, c$ and $d$ are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity $P$ is:
Total percentage error is $\frac{\Delta P}{P} = 3(1\%) + 2(3\%) + 1(2\%) + \frac{1}{2}(4\%) = 3 + 6 + 2 + 2 = 13\%$.
For the relation $P = \frac{a^3 b^2}{c d^{1/2}}$, maximum fractional error is given by: $\frac{\Delta P}{P} = 3\left(\frac{\Delta a}{a}\right) + 2\left(\frac{\Delta b}{b}\right) + 1\left(\frac{\Delta c}{c}\right) + \frac{1}{2}\left(\frac{\Delta d}{d}\right)$. Expressed in percentage errors: $\% \Delta P = 3(1\%) + 2(3\%) + 1(2\%) + \frac{1}{2}(4\%) = 3\% + 6\% + 2\% + 2\% = 13\%$.
2008 AIPMT 1 question
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If the error in the measurement of radius of a sphere is 2 % then the error in the determination of volume of the sphere will be -Volume of a sphere: $V = \dfrac{4}{3}\pi r^3$
Since $V \propto r^3$, the relative error is $\dfrac{\Delta V}{V} = 3\,\dfrac{\Delta r}{r}$
$\dfrac{\Delta V}{V} \times 100 = 3 \times \left(\dfrac{\Delta r}{r} \times 100\right)$
Percentage error in volume = 3 $\times$ percentage error in radius
$= 3 \times 2 = 6$ percent
So the error in the determination of the volume is 6 %.