You measure two quantities as A = 1.0 \; m \pm 0.2 \; m, B = 2.0 \; m \pm 0.2 \; m. We should report correct value for √ AB as:

a) 1.4 \; m \pm 0.4 \; m

b) 1.41 \; m \pm 0.15\; m

c) 1.4 \; m \pm 0.3 \; m

d) 1.4 \; m \pm 0.2\; m

Answers (1)

The answer is the option (d) 1.4\pm 0.2\; m

There are two significant figures in 1.0 & 2.0

\sqrt{AB}=\sqrt{1.0\times 2.0}=\sqrt{2}

=1.414\; m

After roundig up 1.0 &2.0 we het two sigificat features, i.e.

X=\sqrt{AB}

=1.4

Now, \frac{\Delta X}{X}=\frac{1}{2}[\frac{\Delta A}{A}+\frac{\Delta B}{B}]

\frac{\Delta X}{1.4}=0.1\left [ \frac{2.0+1.0}{1.0\times 2.0} \right ]

\Delta X=0.1(\frac{3}{2})((1.4)

=0.21\ m after rounding up

Thus, option (d) is the right answer.

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