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Units and Measurements — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements3 Marks
Question
An experiment measured quantities a, b, c and then x is calculated by using the relation $\text{x}=\frac{\text{ab}^2}{\text{c}^3}$ If the percentage errors in measurements of a, b and care $\pm1\%, \pm2\% \text{ and } \pm 1.5\%$ respectively, then calculate the maximum percentage error in value of x obtained.
✓

Answer

Given:
$\text{x}=\frac{\text{ab}^2}{\text{c}^3}$
$\therefore\Big(\frac{\Delta​​\text{x}}{\text{x}}\Big)_{\text{max}}=\frac{\Delta\text{a}}{\text{a}}+2\frac{\Delta\text{b}}{\text{b}}+3\frac{\Delta\text{c}}{\text{c}}$
But $\frac{\Delta\text{a}}{\text{a}}=\pm1\%,\frac{\Delta\text{b}}{\text{b}}=\pm2\%$
And $\frac{\Delta\text{c}}{\text{c}}=\pm1.5\%$
$\therefore\Big(\frac{\Delta\text{x}}{\text{x}}\Big)_{\text{max}}=1\%+2\times2\%+3\times1.5\%$
$=(1+4+4.5)\%=9.5\%$

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