Question

You measure two quantities as A = (1.0 $\pm$ 0.2) m and B = (2 $\pm$ 0.2) m then what should report correct value for $\sqrt{AB}$ is

• A. (1.41 $\pm$ 0.4) m
• B. (1.4 $\pm$ 0.15) m
• C. (1.4 $\pm$ 0.3) m
• D. (1.4 $\pm$ 0.2) m

Answer 1

The correct option is D (1.4 $\pm$ 0.2) m

According to the problem $A=1.0m\pm 0.2mB=2.0m\pm 0.2m$Let $Z=\sqrt{AB}$

$=\sqrt{\left(1.0\right)\left(2.0\right)}=1.414m$Roiunding of to two significants digits $Z=1.4m$
$\sqrt{AB}=\sqrt{1\times 2}=1.414=1.4$

Relaive error $\frac{\Delta Z}{Z}$ = $\frac{1}{2}(\frac{\Delta A}{A}+\frac{\Delta B}{B})=\frac{1}{2}\times \frac{0.6}{2},=0.15$
$\frac{\Delta Z}{Z}=0.15,\Delta Z=0.210$
Rounding off to one significant digit $\Delta Z=0.2$ $m$
the correct value for $\sqrt{AB}$ = $\left(1.4\pm 0.2\right)m$