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 .......
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(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 $\frac{F_1}{F_2}=\frac{1}{1} \quad$ or $F_1: F_2:: 1: 1$
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