An experiment is carried out to determine the Young modulus $E$ of steel using a vertical wire of initial length $L$ and cross-sectional area $A$ - AQA - A-Level Physics - Question 26 - 2020 - Paper 1

The gradient of the graph of extension against weight represents the relationship between the applied weight (force) and the resulting extension of the wire. According to Hooke's Law, the extension ( ext{extension}) is directly proportional to the applied force (weight), given by the formula:

$ext{extension} = \frac{F}{k}$

where $F$ is the applied force and $k$ is the stiffness constant of the wire.

From this relationship, we know that the Young's Modulus $E$ can be defined as:

$E = \frac{FL}{A \cdot ext{extension}}$

Rearranging this formula, we find that the gradient can be expressed as:

$\text{gradient} = \frac{E A}{L}$

Thus, the correct answer from the options provided is:

C: $\frac{EA}{L}$