Question

A body travels uniformly a distance of $(13.8\pm 0.2)m$ in a time $(4.0\pm 0.3)s$. Calculate its velocity with error limits. What is the percentage error in velocity?

Answer 1

We know that, $V=\frac{D}{T}.............\left(1\right)$

On taking log on both sides and differentiating , we get

$\frac{dV}{V}=\frac{dD}{D}+\frac{dT}{T}..............\left(2\right)$ ( '+' because errors are always added)

From (1)

$V=\frac{13.8}{4}=3.45$

and it is given that $D=13.8,dD=\pm 0.2,T=4.0,dT=\pm 0.3$

Putting the Obtained and Given values , we get

$\frac{dV}{3.45}=\pm (\frac{0.2}{13.8}+\frac{0.3}{4})\Rightarrow dV=\pm (\frac{0.2}{13.8}+\frac{0.3}{4})\ast 3.45=\pm 0.308m/s$

So, $V=3.45\pm 0.308m/s$

Hence, percentage error in velocity

$\frac{dV}{V}=\frac{\pm 0.308}{3.45}\times 100=\pm 8.9\%$