Question

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ___ cm.

Answer 1

$\frac{\frac{F}{A}}{\frac{\Delta L}{L}}$=Y ⇒△L=$\frac{FL}{AY}$ $\frac{△L_2}{△L_1}$=($\frac{F_2}{F_1}$)×($\frac{L_2}{L_1}$)×($\frac{A_1}{A_2}$)
=$\frac{4×4×1}{16}$=1 △L2=△L1=5cm