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

Substituting values from each option:

• Option A: $x_A = \frac{F \cdot 3L}{X \cdot E}$
• Option B: $x_B = \frac{F \cdot L}{2X \cdot E}$
• Option C: $x_C = \frac{F \cdot 3L}{X \cdot 4E}$
• Option D: $x_D = \frac{F \cdot L}{2X \cdot 4E}$

1. For Option A: $x_A = \frac{3FL}{XE}$

2. For Option B: $x_B = \frac{FL}{2XE}$

3. For Option C: $x_C = \frac{3FL}{4XE}$

4. For Option D: $x_D = \frac{FL}{8XE}$

The smallest extension occurs in Option D ($x_D$), where the multiple of the Young's modulus is higher, and the cross-sectional area is larger.

After evaluating all options, the combination of properties that would produce the smallest extension of the wire when the same tensile force is applied is Option D: 2X, L, 4E.