Question

Measure of two quantities along with the precision of respective measuring instrument is $A=2.5\, m s^{-1}\pm0.5\, m s^{-1},B=0.10 s\pm0.01\, s$ The value of $AB$ will be

• A. $\left(0.25\pm0.08\right)m$
• B. $\left(0.25\pm0.5\right)m$
• C. $\left(0.25\pm0.05\right)m$
• D. $\left(0.25\pm0.135\right)m$

Answer 1

Answer: (A)

$A=2.5 \,ms^{-1}\pm 0.5\,ms^{-1},B=0.10\,s \pm 0.01\,s$
$x=AB=\left(2.5\right)\left(0.10\right)=0.25 \,m$
$\frac{\Delta x}{x}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$
$=\frac{0.5}{2.5}+\frac{0.01}{0.10}=\frac{0.05+0.025}{0.25}=\frac{0.075}{0.25}$
$\Delta x=0.075=0.08\, m$
Rounding off to two significant figures.
$AB=\left(0.25 \pm 0.08\right)m$