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Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3 \mathrm{~A}$. If the length of the first wire is increased by $\Delta /$ on applying a force $F$, how much force is needed to stretch the socond wire by the same amount?(1) $4 \mathrm{~F}$(2) $6 \mathrm{~F}$(3) $9 \mathrm{~F}$(4) $\mathrm{F}$
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3 \mathrm{~A}$. If the length of the first wire is increased by $\Delta /$ on applying a force $F$, how much force is needed to stretch the socond wire by the same amount?
(1) $4 \mathrm{~F}$
(2) $6 \mathrm{~F}$
(3) $9 \mathrm{~F}$
(4) $\mathrm{F}$
Physics
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3 \mathrm{~A}$. If the length of the first wire is increased by $\Delta /$ on applying a force $F$, how much force is needed to stretch the socond wire by the same amount?
(1) $4 \mathrm{~F}$
(2) $6 \mathrm{~F}$
(3) $9 \mathrm{~F}$
(4) $\mathrm{F}$

Answer is (3)

Wire 1

Wire 2 :

For wire 1 ,

$\Delta \mathrm{l}=\left(\frac{\boldsymbol{F}}{\mathrm{AY}}\right) \mathbf{3 |}$

For wire 2 ,

$\frac{F^{\prime}}{3 A}=Y \frac{\Delta l}{I}$

$\Rightarrow \Delta \mathbf{I}=\left(\frac{F^{\prime}}{3 A Y}\right)$

From equation (i) \& (ii),

$\Delta \mathbf{l}=\left(\frac{F}{A Y}\right) 3 \mathbf{l}=\left(\frac{F^{\prime}}{3 A Y}\right)$

$\Rightarrow \quad F^{\prime}=9 F$

i

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