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

Answer 1

The correct option is A $(0.25\pm 0.08)m$

Given : $\Delta A=0.5m/s$ $\Delta B=0.01s$

The absolute value of AB $=2.5\times 0.10=0.25m$

Relative error in AB, $\frac{\Delta AB}{AB}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$

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

$⟹\Delta AB=0.075=0.08m$
Thus value of AB is $(0.25\pm 0.08)m$