Q: Measure of two quantities along with the precision of respective measuring instrument is
A = 2.5 ms-1 ± 0.5 ms-1 , B = 0.10 s ± 0.01 s . The value of AB will be
(a) (0.25 ± 0.08)m
(b)(0.25 ± 0.5)m
(c)(0.25 ± 0.05)m
(d)(0.25 ± 0.135)m
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Ans: (a)
Sol: Let x = A B = 2.5 × 0.10 = 0.25
$\displaystyle x = A B $
$\displaystyle \frac{\Delta x}{x} = \pm (\frac{\Delta A}{A} + \frac{\Delta B}{B} ) $
$\displaystyle \frac{\Delta x}{x} = \pm (\frac{0.5}{2.5} + \frac{0.01}{0.10} ) $
$\displaystyle \frac{\Delta x}{x} = \pm (0.3 ) $
$\displaystyle \Delta x = \pm (0.3 )x $
$\displaystyle \Delta x = \pm (0.3 )0.25 = 0.075 = 0.08 $ (Rounding off to one significant figures)
$\displaystyle x + \Delta x = ( 0.25 \pm 0.8 )m $