Question

You measure two quantities A=1.0+_0.2m , B=2.0+_0.2m . We should report correct value for ROOT OF AB as :

A. 1.4m +_ 0.4 m

B. 1.41m +_0.15m

C. 1.4m+_0.3m

D. 1.4m +_0.2m

Answer 1

$$\begin{gathered} A=1.0\pm 0.2m \\ B=2.0\pm 0.2m \\ Letc=\sqrt{AB} \\ C=\sqrt{1\times 2}=\sqrt{2} \\ \frac{∆c}{c}=\frac{1}{2}\left(\frac{∆A}{A}+\frac{∆B}{B}\right) \\ errorin\sqrt{AB}is∆c \\ \frac{∆c}{\sqrt{2}}=\frac{1}{2}\left(\frac{0.2}{1}+\frac{0.2}{2}\right) \\ ∆c=0.2 \end{gathered}$$