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 $\frac{FL}{AY}=\Delta x$
$\{\because \Delta x,Y$ 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 $F_1:F_2::1:1$