Question

a physical quantity X is related to three observable values a b c as X =√a×b^2\c^2the error of measurement in a b c are to percentage 1 percentage and 3 percentage respectively what is the percentage in quantity x​

Answer 1

Answer:

Answer is 9%

Explanation:

∆X/X×100 = 1/2×∆a/a×100 + 2×∆b/b×100 + 2×∆c/c×100

So, ∆X/X×100 = (1/2×2 + 2×1 + 2×3)%

=(1 + 2 + 6)%

=9%

Hope it helps.....

Answer 2

Given :

A physical quantity X is related to three observable values a b c as :

$X= \dfrac{\sqrt{a}b^2}{c^2}$

Percentage error in a,b and c are 2%, 1% and 3% respectively.

To find:

We need to find the percentage error in X.

Solution:

The percentage error in X is given by :

$\dfrac{\Delta X}{X}=\dfrac{1}{2}\dfrac{\Delta a}{a}+2\dfrac{\Delta b}{b}+2\dfrac{\Delta c}{c}\\\\\dfrac{\Delta X}{X}=\dfrac{1}{2}\times 2+2\times 1+2\times 3\\\\\dfrac{\Delta X}{X}=9\%$

So, the percentage error in X is 9 %.

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Percentage error

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