Rankers Physics

Solids: Practice Problem & Solution

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied? (2013)
$\text{Length } = 300 \text{ cm, diameter } = 3 \text{ mm}$
$\text{Length } = 50 \text{ cm, diameter } = 0.5 \text{ mm}$
$\text{Length } = 100 \text{ cm, diameter } = 1 \text{ mm}$
$\text{Length } = 200 \text{ cm, diameter } = 2 \text{ mm}$

Solution Explained:

To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:

Extension $\Delta L = \frac{FL}{AY} = \frac{4FL}{\pi d^2 Y}$. For a given force and material, $$\Delta L \propto \frac{L}{d^2}$$. Calculating $L/d^2$ for the options reveals that option (b) gives the maximum value ($50 / 0.5^2 = 200$).

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