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 $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount ?

• A. F
• B. 9 F
• C. 4 F
• D. 6 F

Answer 1

Answer: (B)

9 F

Answer 2

For wire 1,
$\Delta I = \left(\frac{F}{AY}\right)3I$ ......(i)
For wire 2,
$\frac{F'}{3A} = Y \frac{\Delta I}{I}$
$\Rightarrow \Delta I = \left(\frac{F'}{3AY}\right)I$ ....(iii)
From equation (i) & (ii),
$\Delta I = \left(\frac{F}{AY}\right) 3I = \left(\frac{F'}{3AY}\right)I$
$\Rightarrow F' = 9F$