A metal ruler has thickness $t$. Five measurements of the thickness $t$ at different positions along the length of the ruler are shown below:

$$1.18mm1.24mm1.16mm1.22mm1.20mm$$

Determine the percentage uncertainty in the thickness $t$.

A student wants to determine the Young modulus $E$ of the metal of the ruler in (a).

The student clamps the metal ruler to the edge of a table using a G-clamp. A mass hanger is suspended from the free end of the ruler as shown below.

Draw on this

The Young modulus $E$ of the metal can be determined using the equation:

$$y=\frac{4Mg{L}^3}{w{t}^{3}E}$$

where $M$ is the mass hung from the end of the ruler, $g$ is the acceleration of free fall, $L$ is the length of the ruler extending from the clamp to the point where the mass is hung, $w$ is the width of the ruler, $t$ is the thickness of the ruler, and $y$ is the vertical deflection of the free end of the ruler.

Describe how an experiment may be safely conducted, and how the data can be analysed to determine an accurate value for $E$ using a graphical method.