Which combination of properties would produce the smallest extension of a wire when the same tensile force is applied to the wire? | Cross-sectional area | Length | Young modulus of material | |---------------------|--------|--------------------------| | A | X | 3L | E | | B | 2X | L | E | | C | X | 3L | 4E | | D | 2X | L | 4E | - AQA - A-Level Physics - Question 20 - 2019 - Paper 1

To determine which combination produces the smallest extension, we can use the formula for extension:

$ext{Extension} = \frac{F L}{A Y}$

where:

• $F$ is the tensile force,
• $L$ is the length,
• $A$ is the cross-sectional area,
• $Y$ is the Young's modulus of the material.

From the options:

• In option D: The cross-sectional area is doubled ($2X$), the length is $L$, and the Young modulus is quadrupled ($4E$). This maximizes the resistance to extension. The resulting extension willbe as follows:

$ext{Extension}_D = \frac{F \cdot L}{2X \cdot 4E} = \frac{F}{8X E}$

• In contrast, the other options will yield greater extensions due to lower areas or lower Young's moduli. Thus, option D gives the smallest extension under the same tensile force.