Q. A wire is stretched 1 mm by a force of 1 k N. How far would a wire of the same material and length but of four times that diameter be stretched by the same force ?
A) $\frac{1}{2}\ mm$
B) $\frac{1}{4}\ mm$
C) $\frac{1}{8}mm$
D) $\frac{1}{16}\ mm$
Explanation
(d) $Y = \frac{Fl}{A\mathrm{\Delta}l}\ $
$Y,\ l\ and\ F$ are constants.
$\therefore\ \mathrm{\Delta}l\ \propto \frac{1}{D^{2}}$
$\ \frac{\mathrm{\Delta}l_{2}}{\mathrm{\Delta}l_{1}} = \frac{D_{1}^{2}}{D_{2}^{2}} = \frac{1}{16}$
$\therefore\ \mathrm{\Delta}l_{2} = \frac{1}{16}\ mm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.