PYQ NEET- Mechanical Properties Of Solids L-2

Question: The following four wires are made of same material. Which of these will have the largest extension when the same tension is applied?#

A) Length $=50 \mathrm{~cm}$, diameter $=0.5 \mathrm{~mm}$

B) Length $=100 \mathrm{~cm}$, diameter $=1 \mathrm{~mm}$

C) Length $=200 \mathrm{~cm}$, diameter $=2 \mathrm{~mm}$

D) Length $=300 \mathrm{~cm}$, diameter $=3 \mathrm{~mm}$

Answer: Length $=50 \mathrm{~cm}$, diameter $=0.5 \mathrm{~mm}$#

Sol:#

As $\gamma=\frac{F \times L}{\Delta L \times A}=\frac{m g \cdot L}{\Delta L \cdot A}$ or $\Delta L=\frac{m g L}{\gamma \cdot A}$

$\Rightarrow \Delta L \propto \frac{L}{A}$, which is maximum for option (a).