Question

A body travels uniformly a distance of $\left(13.8\pm 0.2\right)m$ in a time$\left(4.0\pm 0.3\right)s$. The velocity of the body within error limits is

• A. $\left(3.45\pm 0.2\right)m{s}^{-1}$
• B. $\left(3.45\pm 0.3\right)m{s}^{-1}$
• C. $\left(3.45\pm 0.4\right)m{s}^{-1}$
• D. $\left(3.45\pm 0.5\right)m{s}^{-1}$

Answer 1

Answer: (B)

Here, $S=\left(13.8\pm 0.2\right)m$

and $t=\left(4.0\pm 0.3\right)s$

Expressing it in percentage error, we have

$S=13.8\pm \frac{0.2}{13.8}\times 100\%=13.8\pm 1.4\%$

and $t=4.0\pm \frac{0.3}{4}\times 100\%=4\pm 7.5\%$

$\because v=\frac{S}{t}=\frac{13.8\pm 1.4\%}{4\pm 7.5\%}=\left(3.45\pm 8.9\%\right)$
$=\left(3.45\pm 0.03\right)ms$