Question

A body travels uniformly a distance of $(13.8\pm 0.2)m$ in a time $(4.0\pm 0.3)s$. Its velocity with error limits is

• A. $\left(3.5\pm 0.6\right)m{s}^{-1}$
• B. $\left(3.5\pm 0.3\right)m{s}^{-1}$
• C. $\left(6.1\pm 0.6\right)m{s}^{-1}$
• D. $\left(6.1\pm 0.3\right)m{s}^{-1}$

Answer 1

Answer: (B)

Here, $s=\left(13.8\pm 0.2\right)m$, $t=\left(4.0\pm 0.3\right)s$
$\therefore$ veliocity, $v=\frac{s}{t}=\frac{13.8}{4.0}=3.45m{s}^{-1}$
(Rounded off to first place of decimal)
$\therefore \frac{\Delta v}{v}=\frac{\Delta s}{s}+\frac{\Delta t}{t}=\frac{0.2}{13.8}+\frac{0.3}{4.0}$
$=\frac{0.8+4.14}{13.8\times 4.0}=\frac{4.94}{13.8\times 4.0}$
$=0.0865$
or $\Delta v=v\times 0.0865=3.45\times 0.0865$
$=0.3087$.
$\therefore$ velocity $=\left(3.5\pm 0.3\right)m{s}^{-1}$.