Question

A wire stretches by a certain amount under a load. If the load and radius both are increased to four times. The stretch caused in the wire is then

• A. $l$
• B. $\frac{l}{2}$
• C. $\frac{l}{3}$
• D. $\frac{l}{4}$

Answer 1

The correct option is D $\frac{l}{4}$

Young's modulus, $Y=\frac{W}{A}\times \frac{L}{l}$
$\therefore$ Elongation, $l=\frac{WL}{AY}=\frac{WL}{\pi r^{2}Y}$
When both load and radius are increased to four times, the elongation becomes
$l^{\prime }=\frac{4W\times L}{\pi {\left(4r\right)}^{2}Y}=\frac{WL}{4\pi r^{2}Y}=\frac{l}{4}$