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 3A. If the length of the first wire is increased by l on applying a force F, how much force is needed to stretch the socond wire by the same amount?

For wire 1,

$\Delta l = \left(\frac{F}{AY}\right)3l \quad \dots(i)$

For wire 2,

$\frac{F'}{3A} = Y \frac{\Delta l}{l}$

$\Rightarrow \Delta l = \left(\frac{F'}{3AY}\right)l \quad \dots(ii)$

From equation (i) & (ii),

$\Delta l = \left(\frac{F}{AY}\right)3l = \left(\frac{F'}{3AY}\right)l$

$\Rightarrow \boxed{F' = 9F}$