Physical World Units and Measurements - Result Question 41
42. In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C an 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: 42. (b)
Solution:
- (b) Given, $x=\frac{A^{2} B^{1 / 2}}{C^{1 / 3} D^{3}}$
$ \begin{matrix} % \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 \end{matrix} $
$ \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} $
