Two wires of the same material have lengths in the ratio 1 : 2 and their radii a

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

Options:

A . √2:2

B . 2: √2

C . 1 : 1

D . 1 : 2

Answer: Option C
:
C

Y = \frac{F l}{π r^{2} △ l} o r △ l = \frac{F}{π r^{2} y}

△ l \propto \frac{1}{r^{2}}

△ l^{'} \propto \frac{21}{(\sqrt{2} r)^{2}} o r △ l^{'} \propto \frac{1}{r^{2}}

Therefore

\frac{△ l}{△ l^{'}}

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