In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows: P=cda3b2. Percentage error in P is:
A
10%
B
7%
C
4%
D
14%
Step-by-Step Solution
Identify the Given Formula: The quantity P is given by P=cda3b2.
Apply Error Propagation Rules: For a quantity that is a product or quotient of other quantities, the maximum relative error is the sum of the relative errors of the individual quantities multiplied by their respective powers. Thus, PΔP=3aΔa+2bΔb+cΔc+dΔd.
Calculate Percentage Error: Multiplying by 100 converts this to percentage error:
% error in P=3(% error in a)+2(% error in b)+(% error in c)+(% error in d).
Substitute Given Values:% error in P=3(1%)+2(2%)+1(3%)+1(4%)% error in P=3%+4%+3%+4%=14%.
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