You measure two quantities as A = 1.0 m 0.2 m, B = 2.0 m 0.2 m. W… - Vidyadip

MCQ

You measure two quantities as $\text{A} = 1.0 \text{m}\pm 0.2 \text{m},\ \text{B} = 2.0 \text{m}\pm 0.2 \text{m}.$ We should report correct value for $\sqrt{\text{AB}}$ as:

A
$1.4 \text{m}\pm 0.4\text{m.}$
B
$1.41\text{m} \pm 0.15 \text{m}.$
C
$1.4\text{m} \pm 0.3 \text{m}.$
✓
$1.4\text{m} \pm 0.2 \text{m}.$

✓

Answer

Correct option: D.

$1.4\text{m} \pm 0.2 \text{m}.$

According to the problem, $\text{A}=1.0\text{m}\pm0.2\text{m},\ \text{B}=2.0\text{m}\pm0.2\text{m}$
Let, $\text{Z}=\sqrt{\text{AB}}=\sqrt{(1.0)(2.0)}=1.414\text{m}$
Rounding off to two significant digits Z = 1.4m
$\text{AS}\ \frac{\Delta\text{Z}}{\text{Z}}=\frac{1}{2}\frac{\Delta\text{A}}{\text{A}}+\frac{1}{2}\frac{\Delta\text{B}}{\text{B}}$
$=\frac{1}{2}\Big(\frac{0.2\text{m}}{1\text{m}}\Big)+\frac{1}{2}\Big(\frac{0.2\text{m}}{2\text{m}}\Big)=0.15$
$\Rightarrow\Delta\text{Z}=\text{Z}(0.15)=1.4\text{m}(0.15)=0.212$
Rounding off to one significant digit, $\Delta\text{Z}=0.2\text{m}$
The correct value for $\sqrt{\text{AB}}=1.4\pm0.2\text{m}.$

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