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CBSE Class 11-science Answered

expalin all the derivations of chapter-units and measurement
Asked by ABHILASHA | 16 Sep, 2019, 06:58: PM
answered-by-expert 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, begin mathsize 12px style a subscript m e a n end subscript space equals space 1 over n stack sum a subscript i with i equals 1 below and n on top end style
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,    begin mathsize 14px style increment a subscript m e a n end subscript space equals space 1 over n stack space sum with i equals 1 below and n on top open vertical bar increment a subscript i close vertical bar end style
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
 
-------------------------------------------------------------------------
 
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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