Question

Two wires $A$ and $B$ of same material have radii in the ratio $2 : 1$ and lengths in the ratio $4 : 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is

• A. 1 : 1
• B. 2 : 1
• C. 1 : 2
• D. 1 : 4

Answer 1

Answer: (A)

From $\frac{F L}{A Y}=\Delta x$
$\{\because \Delta x, Y$ same $\}$
We using $F \propto \frac{L}{A} \propto \frac{L}{r^{2}}$
So $\frac{F_{1}}{F_{2}}=\frac{L_{1}}{r_{1}^{2}} \times \frac{r_{2}^{2}}{L_{2}}=\left(\frac{L_{1}}{L_{2}}\right) \times\left(\frac{r_{2}}{r_{1}}\right)^{2}$
Substitute the ratio's
We get $\frac{F_{1}}{F_{2}}=\frac{1}{1} $ or $F_{1}: F_{2}:: 1: 1$