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Q.

What is the maximum percentage error in A if $A = \frac{\sqrt{p q}}{r^{2} s^{3}}$ and percentage error of measurement in p, q, r and s are 1%, 3%,0.5% and 0.33% respectively?

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a

3%

b

2%

c

4%

d

0%

answer is C.

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Detailed Solution

$A = \frac{\sqrt{p q}}{r^{2} s^{3}}$ So % erroe in A is given as $\frac{Δ A}{A} \times 100$

$= (\frac{1}{2} \frac{Δ p}{p} + \frac{1}{2} \frac{Δ q}{q} + 2 \frac{Δ r}{r} + 3 \frac{Δ s}{s}) \times 100$

So

$\frac{Δ A}{A} \times 100 = \frac{1}{2} \times 1 + \frac{1}{2} \times 3 + 2 \times 0.5 + 3 \times . 33 = 4 %$

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What is the maximum percentage error in A if A=pqr2s3 and percentage error of measurement in p, q, r and s are 1%, 3%,0.5% and 0.33% respectively?