Question 44: Units , Dimensions and Error Analysis

Question

A quantity Q is formulated as $X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}$. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is

Accepted Answer

The quantity $ Q $ is expressed as $ Q = X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}} $. The variables $ X $, $ Y $, and $ Z $ are independent parameters with fractional errors of 0.1, 0.2, and 0.5, respectively. To determine the maximum fractional error in $ Q $, we can use the following method:
$  	ext{Fractional error in } Q = \left| -2 ight| \frac{\Delta X}{X} + \left| \frac{3}{2} ight| \frac{\Delta Y}{Y} + \left| -\frac{2}{5} ight| \frac{\Delta Z}{Z}  $
Substituting the fractional errors into the equation:
$  = 2 	imes 0.1 + \frac{3}{2} 	imes 0.2 + \frac{2}{5} 	imes 0.5  $
Calculating each term gives:
$  = 0.2 + 0.3 + 0.2  $
Summing these values results in:
$  = 0.7  $
Thus, the maximum fractional error in $ Q $ is 0.7.

Answer

0.6

Answer

0.8

Answer

0.7

Answer

0.1

Units , Dimensions and Error Analysis

A quantity Q is formulated as X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is

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