Question

Four wires made of same materials are stretched by the same load. Their dimensions are given below. The one which elongates more is ?

• A. Wire of length 1 m and diameter 1 mm
• B. Length 2m, diameter 2 mm
• C. Length 3m, diameter 3 mm
• D. Length 0.5m, diameter 0.5mm

Answer 1

The correct option is D Length 0.5m, diameter 0.5mm

$\Delta l=\frac{FL}{Ay}$

$A\to \Delta l=\frac{F\times 1}{y\pi (\frac{1}{2}{)}^2}\times {10}^6=\frac{yF}{\pi y}\times {10}^6$

$B\to \Delta l=\frac{F\times 2}{y\pi 1^2}\times {10}^6=\frac{2F}{\pi y}\times {10}^6$

$C\to \Delta l=\frac{F\times 3\times 4}{y\pi 1}\times {10}^6=\frac{4}{3}\frac{F}{\pi y}\times {10}^6$

$D\to \Delta l=\frac{F\times \frac{1}{2}}{y\pi (\frac{1}{4}{)}^2}\times {10}^6=\frac{8F}{Y\pi }\times {10}^6$

$\Delta l$ of wire D is longest.