A wire Y of cross-sectional area A and length l is joined to a second wire Z of cross-sectional area 2A and length 2l as shown - Edexcel - A-Level Physics - Question 4 - 2023 - Paper 2

To determine the extension of wire Z, we can use Hooke's Law, which states that the extension is proportional to the force applied, the length of the wire, and inversely proportional to the cross-sectional area. This can be represented as:

ext{Extension} (e) = rac{F imes l}{A imes Y}

where:

• $e$ is the extension,
• $F$ is the applied force,
• $l$ is the original length,
• $A$ is the cross-sectional area,
• $Y$ is the Young's modulus of the material.

For wire Y:

• Area, $A = A$
• Length, $l_Y = l$
• Extension, $e_Y = x$

Using Hooke's Law:

x = rac{F imes l}{A imes Y}$$ For wire Z: - Area, $A_Z = 2A$ - Length, $l_Z = 2l$ Using Hooke's Law for wire Z:

e_Z = rac{F imes 2l}{2A imes Y}$$

Now substituting the expression for extension of wire Y into this formula:

e_Z = rac{F imes 2l}{2A imes Y} = rac{1}{2} imes rac{F imes l}{A imes Y} = rac{x}{2}$$ Thus, the extension of wire Z is: $$\frac{x}{2}$$ Therefore, the correct answer is D.