Physical World Units And Measurements Ques 38
38. In an experiment, the percentage of error occurred in the measurement of physical quantities $ A, B, C$ and $ D$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. Then the maximum percentage of error in the measurement $X$, where $X=$ $\frac{A^{2} B^{1 / 2}}{C^{1 / 3} D^{3}}$ will be :
[2019]
(a) $(\frac{3}{13}) \%$
(b) $16 \%$
(c) $-10 \%$
(d) $10 \%$
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Answer:
Correct Answer: 38.(b)
Solution:
- (b) Given, $x=\frac{A^{2} B^{1 / 2}}{C^{1 / 3} D^{3}}$
$ \% \text{ error, } \frac{\Delta x}{x} \times 100=2 \frac{\Delta A}{A} \times 100+\frac{1}{2} \frac{\Delta B}{B} \times 100+\frac{1}{3} \frac{\Delta C}{C} \times 100+3 \frac{\Delta D}{D} \times 100$
$ \begin{aligned} & =2 \times 1 \%+\frac{1}{2} \times 2 \%+\frac{1}{3} \times 3 \%+3 \times 4 \% \\ & =2 \%+1 \%+1 \%+12 \%=16 \% \end{aligned} $
BETA
