Question

Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

• A. L = 100 cm, r = 1 mm
• B. L = 200 cm, r = 3 mm
• C. L = 300 cm, r = 3 mm
• D. L = 400 cm, r = 4 mm

Answer 1

The correct option is A L = 100 cm, r = 1 mm

$\begin{array}{c}\text{L=length of the wire}\\ r=\text{radius of the wine}\\ Y\text{is same for all as made up of}\\ \text{same material}\end{array}$

$Y=\frac{F/A}{\frac{dl}{l}}\Rightarrow dl=\frac{Fl}{AY}=\left(\frac{f}{\gamma }\right)\times \frac{\lambda }{\pi r^2}$

$\begin{array}{cc}\therefore dl& =\frac{cl}{\pi r^2}\\ \therefore \left(\frac{e}{r^2}\right)\uparrow \Rightarrow dl\uparrow & \\ \therefore \text{checking options we get}(L=100cm\&r=\mathrm{lm}m)\text{wire elongate most}& \\ & \end{array}$

Hence option A is correct