Question

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

• A. $(0.25 ? 0.08) \,m$
• B. $(0.25 ? 0.5) \,m$
• C. $(0.25 ? 0.05) \,m$
• D. $(0.25 ? 0.135) \,m$

Answer 1

Answer: (A)

$(0.25 ? 0.08) \,m$

Answer 2

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 $AB ( 0 . 2 5 \pm 0 . 8 ) m$