Write a note on the combination of errors.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) When an experiment involves several measurements,the errors in all individual measurements combine to affect the final result.
For example,in the measurement of density $(d = m/V)$,the errors in the measurement of mass $(m)$ and volume $(V)$ will combine to produce an error in the calculated density.
Errors combine according to the following mathematical operations:
$1$. Addition: If $z = a + b$,then the absolute error $\Delta z = \Delta a + \Delta b$.
$2$. Subtraction: If $z = a - b$,then the absolute error $\Delta z = \Delta a + \Delta b$.
$3$. Multiplication: If $z = ab$,then the relative error $\frac{\Delta z}{z} = \frac{\Delta a}{a} + \frac{\Delta b}{b}$.
$4$. Division: If $z = a/b$,then the relative error $\frac{\Delta z}{z} = \frac{\Delta a}{a} + \frac{\Delta b}{b}$.
$5$. Power: If $z = a^n$,then the relative error $\frac{\Delta z}{z} = n \frac{\Delta a}{a}$.

Explore More

Similar Questions

Write the types of errors in the measurement of a physical quantity and explain them.

Explain the effect of multiplication or division of errors on the final result.

Can error be completely eliminated?

The resistance $R = \frac{V}{I}$,where $V = (50 \pm 2) \; V$ and $I = (20 \pm 0.2) \; A$. The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........

The International Avogadro Coordination project created the world's most perfect sphere using Silicon in its crystalline form. The diameter of the sphere is $9.4 \,cm$ with an uncertainty of $0.2 \,nm$. The atoms in the crystals are packed in cubes of side $a$. The side is measured with a relative error of $2 \times 10^{-9}$,and each cube has $8$ atoms in it. Then,the relative error in the mass of the sphere is closest to (assume molar mass of Silicon and Avogadro's number to be known precisely)

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo