Question

a wire has mass of (0.3 +- 0.003) g , a radius of (0.5 +- 0.005)mm and length (6 +- 0.06)cm. Find the percentage error in the measurment of its density.

Answer 1

The density of the wire is given as:
$$\begin{gathered} \text{Density}=\frac{\text{Mass}}{\text{Volume}} \\ \rho =\frac{M}{\pi R^{2}L} \\ \text{Therefore, the pecentage error in the density}, \\ \frac{∆\rho }{\rho }\times 100=\pm \left(\frac{∆M}{M}+2\frac{∆R}{R}+\frac{∆L}{L}\right)\times 100 \\ =\pm \left(\frac{0.003}{3}+2\times \frac{0.005}{0.5}+\frac{0.06}{6}\right)\times 100=\pm (0.01+0.02+0.01)\times 100=4\% \end{gathered}$$