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  3. Physics
  4. 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

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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

Physical World, Units and Measurements

Solution:

Here, $A =2.5 \,ms ^{-1} \pm 0.5\, ms ^{-1}, B =0.10 s \pm 0.01 \,s$
$AB =\left(2.5\, ms ^{-1}\right)(0.10 s )=0.25 \,m$
$\frac{\Delta AB }{ AB }=\left(\frac{\Delta A }{ A }+\frac{\Delta B }{ B }\right)=\left(\frac{0.5}{2.5}+\frac{0.01}{0.10}\right)=0.3$
$\Delta AB =0.3 \times 0.25 \,m =0.075\, m =0.08 \,m$
(Rounded off to two significant figures)
The value of $AB ( 0 . 2 5 \pm 0 . 8 ) m$