PARAGRAPH "A"
If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x,y and z are 
x, 
y and 
z, respectively, then
The series expansion for 
, to first power in 
, is 
. The relative errors in independent variables are always added. So the error in z will be
The above derivation makes the assumption that 
. Therefore, the higher powers of these quantities are neglected.
(There are two questions based on PARAGRAPH "A", the question given below is one of them)
(i) Consider the ratio 
to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is 
, then what is the error 
in determining r ?
0.04
0.03
0.02
(ii) In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed in the first 1.0s. For |x| < 1, ln(l + x) = x up to first power in x . The error 
, in the determination of the decay constant 
, in s -1 is 0.01
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)
alternate:
(ii)
alternate:
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