Question 1

1. A student determines the resistivity $\rho$ of a metal that is in the form of a cylindrical wire.
   The student makes the following measurements:
   Length $L$ of the wire = $(462 \pm 2)\text{mm}$

Readings for the diameter $d$ of the wire:

Resistance $R$ of the wire = $13.7\,\Omega \pm 1.5\%$

(a) Outline why the measurements of $d$ were made at different places along the wire. [1]

(b) Suggest suitable instruments for the measurement of
(i) $L$ [1]

(ii) $d$ [1]

(c) (i) Show that the mean diameter of the wire is about $0.2\text{mm}$. [2]

(ii) Calculate the fractional uncertainty in the diameter of the wire. [2]

(iii) Calculate the fractional uncertainty in the length of the wire. [1]

(d) The resistivity of the wire is given by $\rho = \frac{RA}{L}$ where $A$ is the cross-sectional area of the wire. Calculate the value of $\rho$ and its absolute uncertainty. State your answers to an appropriate number of significant figures. [3]