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 use the formula for extension in materials subjected to force:

ext{Extension} = rac{F l}{A imes Y}

Where:

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

For wire Y:

• Length, $l_Y = l$
• Cross-sectional area, $A_Y = A$

Thus, the extension $x$ for wire Y is:

x = rac{F l}{A Y} ag{1}

For wire Z:

• Length, $l_Z = 2l$
• Cross-sectional area, $A_Z = 2A$

The extension $x_Z$ for wire Z is:

x_Z = rac{F (2l)}{(2A) Y} = rac{F l}{A Y}

Since we already have that: x = rac{F l}{A Y} This implies:

$$$$

Therefore, wire Z extends by the same amount as wire Y. Thus, the correct answer is:

C x.