Q. Two wires of the same length and same material but radii in the ratio of 1 : 2 are stretched by unequal forces to produce equal elongation. The ratio of the two forces is
A) 1 : 1
B) 1 : 2
C) 2 : 3
D) 1 : 4
Explanation
(d) $Y = \frac{Fl}{A\mathrm{\Delta}l}$
In the given problem, $Y,\ l\ and\ \mathrm{\Delta}l\ $are constants .
$\therefore\ F\ \propto A$
Or $F = \ \pi^{2}\ or\ \ F\ \propto r^{2}\ \ or\ \frac{F_{1}}{F_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{1}{4}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.