Question

Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio 1 : $\sqrt{2}$. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

• A. √2 : 2
• B. 2 : √2
• C. 1 : 1
• D. 1 : 2

Answer 1

The correct option is C 1 : 1

$Y=\frac{Fl}{\pi r^2△l}or△l=\frac{F}{\pi r^{2}y}$
$△l\propto \frac{1}{r^2}$
$△l^{\prime }\propto \frac{21}{(\sqrt{2}r{)}^2}or△l^{\prime }\propto \frac{1}{r^2}$
Therefore $\frac{△l}{△l^{\prime }}$=1