Measure of two quantities along with the precision of respective measuring instrument is&n

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1.Units, Dimensions and Measurement

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Measure of two quantities along with the precision of respective measuring instrument is :-
$A = 2.5\, m/s ± 0.5\, m/s$
$B = 0.10\,s\, ± 0.01\, s$
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

$(0.25 ± 0.135) \,m$

Solution

Let $y=\mathrm{AB}$

$\frac{\Delta y}{y}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$

$y=2.5 \times 0.1=0.25$

$\frac{\Delta y}{0.25}=\frac{0.5}{2.5}+\frac{0.01}{0.10}$

$\Rightarrow \Delta \mathrm{y}=0.075=0.08(2 \mathrm{SF})$

Standard 11

Physics

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