Measure of two quantities along with the precision of respective measuring instrument is
$A = 2.5 m s^{- 1} \pm 0.5 m s^{- 1}$ , $B = 0.10 s \pm 0.01 s$
The value of AB will be

(0.25 \pm 0.08) m

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(0.25 \pm 0.8) m

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(0.25 \pm 0.05) m

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(0.25 \pm 0.135) m

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Solution

The correct option is B $(0.25 \pm 0.8) m$
Here, $A = 2.5 m s^{- 1} \pm 0.5 m s^{- 1}$ , $B = 0.10 s \pm 0.01 s$
$A B = (2.5 m s^{- 1}) (0.10 s) = 0.25 m$
$\frac{Δ A B}{A B} = (\frac{Δ A}{A} + \frac{Δ B}{B}) = (\frac{0.5}{2.5} + \frac{0.01}{0.10}) = 0.3$
$Δ A B = 0.3 \times 0.25 m = 0.075 m = 0.08 m$
(Rounded off to two significant figures)
The value of AB $(0.25 \pm 0.8) m$

Suggest Corrections

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