CBSE Class 11-science Answered
expalin all the derivations of chapter-units and measurement
Asked by ABHILASHA | 16 Sep, 2019, 06:58: PM
Expert Answer
For any measurement , in order to consider the accuracy, we need to take n number of measurements and get average.
We also make sure the accurate value is with in some range of values.
Let a1 , a2 .........an are n number of measurements .
Then mean value amean is given by,
error in each measurement is Δa1 = a1 - amean , Δa2 = a2 - amean , ......................, Δan = an - amean etc
error in individual measurement mentioned above may be positive or negative.
Mean absolute error Δamean is given by,
Hence any measurement is likely to lie between a+ Δamean and a-Δamean
Relative error in measurement = Δamean / amean
percentage error δa = ( Δamean / amean ) × 100
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Combination of error
(1) Sum or difference of measured quantities
Let A and B are measured quantities with absolute error ΔA and ΔB.
If we are intersted z = A+B or z = A-B, then absolute error Δz is given by, Δz = ΔA + ΔB
( absolute errors always added, irrespective of sum or difference of measurements )
(2) product or quotient of measurements
if the interested quantity z = A×B or z = A/B , then relative error Δz/z is given by, Δz/z = ( ΔA/A ) + ( ΔB/B )
(3) power of measured quantity
if the interested quantity z = An , then relative error Δz/z is given by, Δz/z = n×( ΔA/A )
Answered by Thiyagarajan K | 19 Sep, 2019, 12:59: PM
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