Question

A physical quantity X=A²B³/C√D, If the percentage errors of measurement in A,B,C and D are 4%,2%,3%and 1% respectively then calculate percentage error in X.

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Answer 1

Answer:

The percentage error in X is $17.5 \%$

Explanation:

Given a physical quantity

                  $X=\frac{A^{2}B^{3} }{C \sqrt{D} }$

 percentage errors of A, B, C and D are $4\%, 2\%, 3\%$ and $1\%$ respectively

Percentage error is the difference between an observed value and the exact value of any quantity, calculated as the percentage of an exact value.

Percentage error is given by the formula:

                    $\frac{observed \ value-exact\ value}{exact \ value} \times 100$

The percentage error in X is

              $\frac{\Delta X}{X} \times 100=\Big[2\frac{\Delta A}{A} \times 100+3\frac{\Delta B}{B}\times 100+\frac{\Delta C}{C} \times 100+\frac{1}{2} \frac{\Delta D}{D} \times 100 \Big]$

                              $=\Big[2 \times 4\%+ 3 \times 2\%+1 \times 3\%+\frac{1}{2} \times 1\% \Big]$

                              $=8\%+ 6\%+ 3\%+\frac{1}{2} \%$

                              $=17.5 \%$

Therefore, the percentage error in X is $17.5 \%$