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1.Units, Dimensions and Measurement
normal
બે રાશિના મૂલ્યો સાધનથી ચોકચાઈ પૂર્વક માપતા $A = 2.5\,m{s^{ - 1}} \pm 0.5\,m{s^{ - 1}}$, $B = 0.10\,s \pm 0.01\,s$ મળે છે. તો $AB$ નું માપન કેટલું થાય?
A$\left( {0.25 \pm 0.08} \right)\,m$
B$\left( {0.25 \pm 0.5} \right)\,m$
C$\left( {0.25 \pm 0.05} \right)\,m$
D$\left( {0.25 \pm 0.135} \right)\,m$
Solution
Error in $AB$
$=\pm\left(\frac{\Delta \mathrm{A}}{\mathrm{A}}+\frac{\Delta \mathrm{B}}{\mathrm{B}}\right) \mathrm{AB}=\pm\left[\frac{0.5}{2.5}+\frac{0.01}{0.10}\right][0.25]$
$=\pm 0.075=\pm 0.08$
Therefore $A B=(0.25 \pm 0.08) m$
$=\pm\left(\frac{\Delta \mathrm{A}}{\mathrm{A}}+\frac{\Delta \mathrm{B}}{\mathrm{B}}\right) \mathrm{AB}=\pm\left[\frac{0.5}{2.5}+\frac{0.01}{0.10}\right][0.25]$
$=\pm 0.075=\pm 0.08$
Therefore $A B=(0.25 \pm 0.08) m$
Standard 11
Physics
