In the measurement of a physical quantity `X = A^(2)B/C^(1//3)D^(3)` The percentage errors introduced in the measurement of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then, the minimum amount of percentage error in the measurement of X is contributed by

Options

A. A
B. B
C. C
D. D

Answer

C

Explanation

`X = A^(2)B/C^(1//3)D^(3)`
Percentage of error in X is given by,
`DeltaX/X = 2DeltaA/A + Delta B/B + 1/3 DeltaC/C + 3Delta D/D`
=`2(DeltaA/A xx 100%) + (DeltaB/B xx 100%) + 1/3 (DeltaC/C xx 100%) + 3(DeltaD/D xx 100%)`
= 2(2)+ (2) + 1/3 (4) + 3(5) = 4+2+1.1+15
` :.` The minimum percentage error is contributed by 'C'. i.e., 1.1%