Question

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?

Accepted Answer

**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),**

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

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