Question

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

• A. $\left(0.25\pm 0.08\right)m$
• B. $\left(0.25\pm 0.5\right)m$
• C. $\left(0.25\pm 0.05\right)m$
• D. $\left(0.25\pm 0.135\right)m$

Answer 1

Answer: (A)

$A=2.5m{s}^{-1}\pm 0.5m{s}^{-1},B=0.10s\pm 0.01s$

$x=AB=\left(2.5\right)\left(0.10\right)=0.25m$

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

$=\frac{0.5}{2.5}+\frac{0.01}{0.10}=\frac{0.05+0.025}{0.25}=\frac{0.075}{0.25}$

$\Delta x=0.075=0.08m$

Rounding off to two significant figures.

$AB=\left(0.25\pm 0.08\right)m$