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

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

Answer 1

Answer: (D)

$\frac{l}{4}$

Answer 2

: 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

$l' = \frac{4W \times L}{\pi(4r)^{2} \times Y} = \frac{WL}{4\pi r^{2}Y} = \frac{l}{4}$