Question

You measure two quantities as

$A = 1.0m \pm 0.2m,B = 2.0m \pm 0.2m.$ We should report correct value for $\sqrt{AB}$as

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

Answer 1

Answer: (D)

$1.4m \pm 0.2m$

Answer 2

Here, $A = 1.0m \pm 0.2m,B = 2.0m \pm 0.2m$

$\mathrm { AB } = ( 1.0 \mathrm {~m} ) ( 2.0 \mathrm {~m} ) = 2.0 \mathrm {~m} ^ { 2 }$ $\sqrt{AB} = \sqrt{2.0}m = 1.414cm$

Rounding off to two significant figures, we get

$\sqrt { \mathrm { AB } } = 1.4 \mathrm {~cm}$ $\frac{A\sqrt{AB}}{\sqrt{AB}} = \frac{1}{2}\left( \frac{\Delta A}{A} + \frac{\Delta B}{B} \right) = \frac{1}{2}\left( \frac{0.2}{1.0} + \frac{0.2}{2.0} \right) = \frac{0.3}{2}\Delta\sqrt{AB} = \frac{0.3}{2} \times \sqrt{AB} = \frac{0.3}{2} \times 1.414 = 0.212m$Rounding off to one significant figures , we get

$\Delta\sqrt{AB} = 0.2m$

The correct value for $\sqrt{AB}is1.4m \pm 0.2m$