Physical World Units and Measurements - Result Question 44
45. 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 $P=\frac{a^{3} b^{2}}{c d} %$ error in $P$ is:
(a) $10 %$
(b) $7 %$
(c) $4 %$
(d) $14 %$
[2013]
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Answer:
Correct Answer: 45. (d)
Solution:
(d) Given, $P=\frac{a^{3} b^{2}}{c d}$
Therefore, $\frac{\Delta P}{P} \times 100 %=3 \frac{\Delta a}{a} \times 100 %$
$+2 \frac{\Delta b}{b} \times 100 %+\frac{\Delta c}{c} \times 100 %+\frac{\Delta d}{d} \times 100 %$
$=3 \times 1 %+2 \times 2 %+3 %+4 %=14 %$
When we multiply or divide two measured quantities, the relative error in the final result is equal to the sum of the relative errors in the measured quantities. And when we add or subtract two measured quantities the absolute error in the final result is equal to the sum of the absolute error in the measured quantities.
